Conjugate Math – Explanation and Examples

Please don't hate me for posting this Mods lol.
So, basically I have 5 months until I start college. Recently, I have made it a challenge to myself and my abilities to see how much math I can really handle.
To be honest, I've always been mediocre at math, but math has never ceased to amaze me with all its equations and levels of complexity. And I've also realized that it was mainly by lack of focus, dedication, diligence, patience, and commitment which has deterred my progress in math, not so much my intelligence (so I believe haha).
However, now that I've been reinvigorated to confront the new possibilities that await through the process of learning, I'm ready for a disciplined approach to not just understanding maths, but absorbing and utilizing the concepts of math fundamentally. In doing so, I've laid out a path to follow: from basic Algebra to college level stuff like Calc 3 and Differential Equations. This is the exact order and listing from calcworkshop.com, the resource I'll be making tremendous use of on this adventure. For anyone interested in an intuitive and simple to comprehend way of teaching, I highly suggest you check out the website (albeit it is a paid subscriber platform).
I obviously do not intend to finish this entire monstrosity of a course/program/ultimate math killer bootcamp or even half of it, but the crucial thing is that we try our best everyday in pursuit of some arbitrary (or specific) ,personal (or public) goal. And I don't think I'm naive either in thinking I'll just be able to breeze past difficult topics in just 5 months. On the contrary, I am more so inclined to master the basic fundamentals like algebra, trig, precalc than to half-heartedly tackle obscure problems in Linear Algebra just for the sake of doing "hard shit." I think most of you can agree that in order to do well in math or anything, it is paramount for one to build a strong foundation on which more complexity can be built.
So that is indeed my plan. I'm guessing I'll spend roughly 4 hours a day adhering to this. Currently, I'm on 1 (Algebra) D (Polynomials) and I'm excited to see where I'll end up in the coming weeks and months. I'm also trying to get better at programming as well during all this. So I'm doubly excited for all the challenges that lie at my feet, just waiting for me to snuggle up and devour them.
But why am I posting this to all you mathematical folks on this subreddit? Well, I have to admit, sometimes Reddit really fuels me to take fruitful actions. And by that I mean you guys motivate me a lot. Especially on those self-improvement subs, I see countless of people getting back on their feet after months or years of depressive, suicidal, and chaotic times. In a way, I'm doing this to make myself feel in tune with the potentiality of my existence (lol Jordan Peterson fans where you at?) by confronting something hard, that could possibly be useful, disguised as fear and illusion. It's 3am here, and I'm rather tired after spending the last few hours typing this gargantuan list up. But even if the following guide can help some of you folks who are struggling to find a direction, whether it's in math or in life, then I'm happy.
It's really just fun and games at the end. To be able to sit here and do math in order to educate myself with amazing resources at my disposal, as the world just keeps innovating and progressing (cough singularity is near cough), is a real dream for some folks. And if I could elaborate on this further, I'd say that there is a meaning or purpose to be found implicit in the act of doing something worthwhile, as challenging and as exhausting as it may be. Right between the lines of aptitude and stress is where we are able to flourish and grow.
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• 1. Algebra
  • A. Intro Algebra
    • Order of Operations
    • Real Numbers
    • Translating Algebraic Expressions
    • Algebraic Properties
    • Multiplying and Dividing
    • Combining Like Terms
    • Consecutive Integers
  • B. Solving Equations
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    • Linear Word Problems
    • Literal Equations
    • Absolute Value
    • Linear Inequalities
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  • C. Exponents
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  • E. Factoring
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    • Trinomial Coefficient One
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    • Factor by Grouping
    • Factoring Cubes
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    • Factoring Word Problems
  • F. Rationals
    • Rational Expressions
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    • Dividing Fractions
    • Adding Fractions
    • Long Division
    • Proportion
    • Solving Equations
    • Percents
    • Graphing Linear Equations
    • Coordinate Plane
    • Finding Intercepts
    • Slope Formula
    • Slope Intercept Form
    • Parallel Perpendicular Lines
    • Point Slope Form
    • Graphing Linear Inequalities
  • G. Systems of Equations
    • Graphing Method
    • Substitution Method
    • Elimination Method
    • System of Inequalities
    • Linear Programming
    • Nonlinear Systems
  • H. Radicals
    • Square Root
    • Rational Exponents
    • Rationalizing
    • Multiplying Radicals
    • Conjugate Math
    • Solving Radical Equations
    • Completing the Square
    • Quadratic Formula
    • Pythagorean Theorem
  • I. Functions & Statistics
    • Relations and Functions
    • Set Notation
    • Linear Function
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    • Z Score
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• 2. Trigonometry (Pre-calc Part 1)
  • A. Trigonometric Functions
    • Interval Notation
    • Coterminal Angles
    • Reference Triangles
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    • Degrees Minutes Seconds
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  • B. Radian Measure
    • Degrees to Radians
    • Arc Length Formula
    • Unit Circle
    • Angular and Linear Velocity
  • C. Graphing Trig Functions
    • Graphing Sine and Cosine
    • Graphing Sine and Cosine with Period Change
    • Graphing Sine and Cosine with Phase Shift
    • Graphing Reciprocal Trig Functions
  • D. Trig Identities
    • Fundamental Trigonometric Identities
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    • Proving Trig Identities
    • Sum and Difference Identities
    • Double Angle Identities
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    • Product-Sum Identities
  • E. Trig Equations
    • Inverse Functions
    • Inverse Trig Functions
    • Solving Trigonometric Equations
    • Solving Trig Equations Using Inverses
  • F. Law of Sines and Cosines
    • Law of Sines
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    • Law of Cosines
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    • What is a Vector?
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    • Complex Numbers in Standard Form
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    • De Moivre’s Theorem
• 3. Math Analysis (Pre-calc Part 2)
  • A. Intro Math Analysis
    • Solving Equations
    • Solving Inequalities
    • Absolute Value Equations
  • B. Functions and Graphs
    • Transformations of Functions
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    • Domain of Composite Functions
  • C. Exponentials and Logarithms
    • Exponential Equations
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  • D. Polynomial Function
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  • E. Rational Functions
    • Identifying Asymptotes
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    • Variation Equations
    • Rational Functions in Calculus
    • Partial Fractions
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  • G. Series and Sequences
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    • Mathematical Induction
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• 4. Calculus 1
  • A. Limits
    • Finding Limits Graphically
    • Limit Rules
    • Squeeze Theorem
    • Limits at Infinity
    • Limits Review
    • Epsilon Delta Definition
    • Limits and Continuity
    • Limits Definition of Derivative
  • B. Derivatives
    • Definition of Derivative
    • Power Rule
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    • Chain Rule
    • Derivative Rules
    • Derivative of Exponential Function
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    • Trig Derivatives
    • Inverse Trig Derivatives
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    • Derivative of Inverse Functions
    • Implicit Differentiation
    • Higher Order Derivatives
    • Logarithmic Differentiation
    • L’Hopital’s Rule
    • Particle Motion
    • Rate of Change
    • Equation of Tangent Line
    • Linear Approximation
    • Continuity and Differentiability
    • Derivatives Using Charts
    • Limit Definition of Derivative
    • Newton’s Method
    • Related Rates
  • C. Application of Derivatives
    • Application of Derivatives Lesson 1
    • Application of Derivatives Lesson 2
    • Application of Derivatives Lesson 3
    • Demand Function
    • Elasticity of Demand
  • D. Integrals (Same as Calc 2, A)
    • Riemann Sum
    • Sigma Notation
    • Integration Rules
    • Trig Integrals
    • Fundamental Theorem of Calculus
    • U Substitution
    • Arc Length Formula
    • Mean Value Theorem for Integrals
    • Particle Motion
    • Simpson’s Rule
    • Partial Fraction Decomposition
    • Integration by Parts
    • Advanced Trigonometric Integration
    • Trig Substitution
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• 5. Calculus 2
  • A. Integrals (Same as in Calc 1)
  • B. Application of Integrals
    • Area Between Two Curves
    • Volumes with Known Cross Sections
    • Solids of Revolution - Disk and Washer Method
    • Solids of Revolution - Shell Method
    • Work and Hooke’s Law
    • Moments and Center of Mass
  • C. Differential Equations
    • Separable Differential Equations
    • Slope Fields
    • Exponential Growth and Decay
    • Euler’s Method
    • Logistic Differential Equations
  • D. Polar Functions
    • Polar Coordinates
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  • E. Parametric and Vector Functions
    • Vectors Lesson
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  • F. Sequences and Series
    • Sequences and Series Intro
    • Nth Term Test
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    • Sequences and Series Review
    • Radius and Interval of Convergence
    • Power Series
    • Maclaurin and Taylor Series Intro
    • Taylor Series
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    • Lagrange Error Bound
• 6. Calculus 3
  • A. Vectors and The Geometry of Space
    • Three-Dimensional Coordinate Systems
    • Vectors in 3D
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    • Equations of Lines and Planes
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  • B. Vector Functions
    • Vector Functions and Space Curves
    • Derivatives and Integrals of Vector Functions
    • Arc Length and Reparameterization
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  • C. Partial Derivatives
    • Functions of Several Variables
    • Limits and Continuity
    • Partial Derivatives
    • Tangent Planes and Linear Approximations
    • Multivariable Chain Rule
    • Directional Derivatives and Gradient Vectors
    • Relative Extrema
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  • D. Multiples Integrals
    • Double Integrals over Rectangles
    • Average Value and Double Integral Properties
    • Iterated Integrals
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    • Double Integrals in Polar Coordinates
    • Applications of Double Integrals: Density, Mass and Moments of Inertia
    • Surface Area
    • Triple Integrals
    • Triple Integrals in Cylindrical Coordinates
    • Triple Integrals in Spherical Coordinates
    • Change of Variables in Multiple Integrals
  • E. Vector Calculus
    • Vector Fields
    • Line Integrals
    • Review of Line Integrals
    • The Fundamental Theorem of Line Integrals
    • Green’s Theorem
    • Curl and Divergence
    • Parametric Surfaces and Their Areas
    • Surface Integrals
    • Stoke’s Theorem
    • The Divergence Theorem
    • Vector Calculus Review
• 7. Linear Algebra
  • A. Linear Equations
    • System of Linear Equations
    • Reduced Row Echelon Form
    • Vector Equations for Matrix Algebra
    • The Matrix Equation Ax=b
    • Solution Sets of Linear Systems
    • Linear Independence
    • Linear Transformations
    • Applications of Linear Systems
  • B. Matrix Algebra
    • Matrix Operations and Determinants
    • Inverse Matrix
    • Invertible Matrix Theorem
    • Partitioned Matrices
    • Matrix Factorization
    • Applications to Computer Graphics
  • C. Determinants
    • Determinant of a Matrix
    • Cramer’s Rule
  • D. Vector Spaces
    • Vector Spaces and Subspaces
    • Null, Column, and Row Spaces
    • Linearly Independent Sets and Bases
    • Coordinate Systems and The Dimensions of a Vector Space
    • Rank
    • Change of Basis
    • Markov Chain Applications
  • E. Eigenvalues and Eigenvectors
    • Eigenvalues and Eigenvectors
    • The Characteristic Equation
    • Diagonalization
    • Eigenvectors and Linear Transformations
    • Complex Eigenvalues
  • F. Orthogonality and Least Squares
    • Inner Product, Length and Orthogonality
    • Orthogonal Sets
    • Orthogonal Projections and Decomposition
    • The Gram-Schmidt Process and QR Factorization
    • Least-Squares Problems
    • Applications to Linear Models: Least-Squares Lines
    • Inner Product Spaces
  • G. Symmetric Matrices and Quadratic Forms
    • Diagonalization of Symmetric Matrices
    • Matrix of the Quadratic Form
• 8. Differential Equations
  • A. Intro to DiffEqs
    • Ordinary Differential Equations
    • Initial Value Problems
  • B. First Order Differential Equations
    • Directional Fields
    • Separable Equations
    • Euler’s Method
    • First Order Linear Differential Equation
    • Solving Exact ODEs
    • Homogeneous Differential Equation
    • Bernoulli Differential Equation
    • Linear and Nonlinear Models
  • C. Second Order Differential Equations
    • Distinct Real Roots
    • Complex Roots
    • Repeated Roots
    • Wronskian
    • Undetermined Coefficients
    • Differential Operators
    • Variation of Parameters
    • Cauchy Euler Equation
    • Predator Prey Models and Electrical Networks
    • Mechanical Vibrations
  • D. Series Solutions
    • Power Series
    • Series Solutions
  • E. Laplace Transform
    • Laplace Transform Overview
    • Inverse Laplace Transforms
    • Initial Value Problems with Laplace Transforms
    • Translation Theorems of Laplace Transforms
  • F. Systems of Differential Equations
    • Homogeneous Linear Systems
    • Phase Plane Portraits

Hey all! I’m trying to find the limit as t-> 7
Here’s the equation: (sqrt(2t+11) - 5) / (t-7)
Here’s where I got stuck. I know that I have to multiply by the conjugate but I don’t know the full output. An online calculator says:
(sqrt(2t+11) - 5) / (t-7) ->
(2t-14) / (sqrt(2t+11) - 5) / (t-7)
Why and how on earth did the - 14 within the term (2t-14) appear after multiplying by the conjugate?
Thanks for your time!

What is the complex conjugate of z=(2+i)e^-ikt?
I know e^-ikt becomes e^ikt using Euler’s, but I’m not sure what to do with the (2+i) that’s multiplied. Do I just switch all the signs and make it (2-i)e^ikt? If not, how do I go about this?
Thank you!

Tell us your questions about stuff like irregular french conjugation maths or just a movie plot you dont get.
Treat others with respect and dont judge them for not knowing something

Complex conjugate of iⁱ
Very simple question on my problem set, but my textbook doesn't give a definite answer to this and googling hasn't helped. Thanks

https://archive.org/details/magnetism1small

Question: https://imgur.com/wJQpWO0
Answer: https://imgur.com/aLOTb9F
Can't understand how they got the left hand side.
Help appreciated, cheers.

So I've been taught that if, for example, 1 + i is a root of a polynomial, then 1 - i is also definitely a root. I was never taught WHY this is true, and wherever I search it up shows some overly complicated explanation with math symbols I've never seen before. So, why is this always true?
(I probably could've found a better sub for this but since complex conjugates come up occasionally in the SAT I came here)

I think I'm getting confused between the fundamental theorem of algebra and conjugate root theorem.
http://imgur.com/a/U2H2h
Q1)part e) I got (z-2-i)(z-i)(z+i) which was correct. The fundamental theorem of algebra says that there will be 3 complex factors which is true. But the conjugate root theorem says that a factor's conjugate will also be a factor. However for (z-2-i), we don't have its conjugate as a factor, why?
For example 22: the complex factor's conjugate is not stated?
Is there something I'm misinterpreting completely wrong?
Thanks

http://imgur.com/a/S4MQP
For this example, I'm confused how the conjugate root theorem can apply here. z³ = 1, isn't this a real number constant, not a real number coefficient?
Since it's not a coefficient, therefore the conjugate root theorem is not applicable here? Or am I missing something obvious?
Thanks

Hi I am new to this subreddit and I hae a question on this particular math problem:
limit of √(x²+10x)-x as x approaches inifinity. I multiplied both the top and bottom by √(x²+10x)+x, and it left the top with 10x. Then I don't know how to deal with the denominator. I know the answer is 5, but I don't know how to get there.
Help!

Example:
√(12+3√4)+√(12-3√4)
The radicands are different, obviously, but only by a factor of -1.
Thanks Reddit for all your help in advance.

Hey HH, I've got a complex numbers problem that I can't seem to figure out.
Question: If z=x+yi Find the values for x and y such as that z-1/z+1=z+2
i is the complex number in this situation. I've understood that to find x & y, a simultaneous equation must occur to find these values but I have difficulty putting into that form. Any help or advice would be greatly appreciated, thank you.

Really stuck with this question here that involves a bit of algebra: http://i.imgur.com/boNnI4N.png
The answer is x = -1 and y = + or - sqrt2
I've tried using null factor law, keeping z as it is, and next, the same thing changing z into x + y.
Would really like some guidance cause I'm quite stumped.

[Connectyx (OTC-PINK: CTYX). Will change to Curative Biotechnology with ticker $CURB in Q1 2021.]
I posted this on pennystocks yesterday.
Full Disclosure: I have a $6k initial position in this stock at a cost average of $.06. The stock is now at $0.155 (as of 2/6/21) with my position at $15.5k and movement is just starting.
I am not a financial advisor. I am simply a broke graduate student interested in investing and fucking retiring early. This post represents my personal views and should not be taken as financial advice. Do your own damn research and stop pumping your hard-earned cash into trending stocks on Reddit posts that are nothing but hype, rocket emojis, and a mob chat jerking each other off. Also, not a doctor! The medical content below should never be a substitute for professional medical advice.
With that said, $CTYX is going to fucking Pluto 🚀🚀🚀🚀🚀🚀 🌑
Price Target: $0.5 by May 1, 2021; $1.25 - $3.00 (~10x) within 2 years with credible potential to be listed on NASDAQ.
This company is absolutely solid on all sides: healthy financials, an experienced & reliable management team, favorable market conditions with a reasonable business model, a solid lineup of products in its pipeline, and many large announcements anticipated within the next 3 months. Simply put, there is extreme asymmetric upside.
$CTYX or Connectyx was taken over by its current team led by CEO Paul Michaels around Feb 2020. Within a year, this CEO has kept every promise he's made and established the infrastructure for growth. The company specializes in bringing orphan drugs (more on this below) through clinical trials and then to market. Paul and his team have decades of experience in big pharma, biotech research, finance, and drug licensing/development (in-depth description in the Management Team section below). They've vetted 3 promising drug candidates in under a year and promised to start clinical trials by mid-2022. If any one of these pass phase 1/2 trials, the market cap grows by hundreds of millions. They also have a reasonable chance to obtain a Priority Review Voucher (PRV) from the FDA that is worth $100-$300M from their strategic picks. They have a clean balance sheet, acquired non-dilute bridge financing while putting these drugs through trials, and have plans of additional deals in the near future.
Why orphan drugs? Orphan drugs are therapeutics that treat rare diseases (defined as illnesses affecting less than 200k Americans per year). From the Orphan Drug Act, there are multiple incentives given by the government to develop orphan drugs: (1) significant tax credits (2) longer market exclusivity after approval (3) waiver of certain FDA fees (4) easier & faster approval process. In 2019, the global orphan drug market is estimated to be valued at $151B. By 2027, this is projected to reach $340.84B (10% compounded annual growth). This the cornerstone of their business model. By gathering a group of experts, they can cheaply vet high potential candidates to add to their development pipeline and then commercialize them from reduced fees as well as fast-track benefits from the FDA.
So why the hell is it call Connectyx? It is just the old name of a software services company which the team acquired. The company has filed for a name change that will be granted within the next 2 weeks to Curative Biotechnology Inc. with a new ticker $CURB. In addition, the CEO himself has hinted at an uplisting to $OTCQB (a certification upgrade from current pink sheet status), mergeacquisition announcements, and $100M in non-dilutive funding. The official FINRA announcement of the name change will be the catalyst for the additional news.
Some quick notes about the charts. The 15x jump in the past couple of months is only the beginning. There is a clear trend of resistance breakthroughs and medium-term consolidation after each announcement. Volatility is low, the number of outstanding shares is small, and there is limited dilutive potential for an OTC.
Let's dive deeper into this hidden gem.
All-Star Management Team
CEO Paul Michaels
Curative BioTech lucked out with a CEO with 25 years of experience in investment banking with a focus on life sciences. Paul has an impressive record, starting as the Executive Vice President and board member of Global Capital Group (a Wall Street wealth management firm). He also got extensive experience in big Pharma through Inabata & Co. Ltd, a subsidiary of a large Japanese drug company, Sumitomo Chemical Group, which totaled $21.8B in revenue in 2013 and employs over 30k people. While serving as Inabata's CFO, Paul licensed American drugs (some from Gilead) for the Asian market. After, the guy helped create Nobelpharma, an orphan drug company, which licenses drugs for rare diseases and got over $35M in initial capital.
In February 2020, Paul took over Connectyx (a software services company at the time) and made it an orphan drug company. It is extremely rare for pink-sheet companies to have such high-caliber, established talent as a leader: decades of experience with finance and leadership positions in multi-billion dollar pharmaceutical companies. He helped build up Inabata and Nobelpharam (both thriving today), and I am confident in his ability to do it again with Connectyx.
VP Communications Pam Bisikirski
Recently, Curative announced Pam as the new Vice President of Communications. She previously served as the director of marketing of National Vision for 21 years. National Vision ($EYE) is a huge optical retail, eye care, and eye-ware company that is trading near a $4B market cap on NASDAQ.
Scientific Advisory Board
Dr. Michael Grace [news] - Ph.D. in Biochemistry and BS in Chemistry from the University of Nebraska. 30 years of experience in BioPharma with top roles in names like Procter & Gamble, Schering-Plough, Bristol-Myers Squibb, NPS Pharma, and Advaxis Immunotherapies. Lead 6 products to registration and commercialization.
Dr. Ronald Bordens [news] - Ph.D. in Biotechnology with over 26 publications and over 2000 citations. 40 years in biotech and big pharma in research & development. Had a fruitful 26-year career at Schering-Plough Research.
Richard Garr [news] - Serves as Director and CEO as well as President of Neuralstem Inc. (now Seneca Biopharma, Inc. which is listed on NASDAQ as $SNCA) for 20 years. Advocate for right to try treatments in the US and Europe. Founded Access Hope CRO (contract research organization) which dedicates itself to this cause. Was founder and current Board Member of the First Star Foundation Mid-Atlantic chapter which focuses on ill children (including pediatric brain cancer).
Robust Drug Pipeline
Keep in mind this company became a biotech firm in Feb 2020 and they already have 3 drugs in the pipeline along with exclusive rights licenses. Insane.
1) IMT504 immune therapy to treat late-stage rabies.
(11/23/2020 Announcement implies IMT504 rabies license deal is complete)
Strategic relationship with Mid-Atlantic BioTherapeutics, Inc. announced on 8/27/2020. Acquired all rights for development of this patented immunotherapy to treat late-stage rabies (a disease with 100% fatality rate after the treatable period, [kills 59k](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6613553/#:~:text=about this topic%3F-,Each year%2C rabies causes approximately 59%2C000 deaths worldwide%2C including approximately,of postexposure prophylaxis (PEP).).)) globally per year).
Now, the value of this may not be in the drug approval itself (although passing trials would be a huge asset of course). The value is the potential in CTYX obtaining a Priority Review Voucher (PRV). These coupons are handed out by the FDA each year to incentivize research into rare diseases. Exercising the coupon means diminishing the approval process from 10 months to 6 after trials. Further, you can freely sell these on a secondary market to other companies! Historically, these have been sold between $100M to $300M each. If obtained, this is an instant 2x-6x increase to its current $50M market cap. There's more.. notice that the FDA has added Rabies to its PRV-eligible tropical diseases list. Currently, there is only a handful of rabies therapies being researched. This means there's actually a good chance of CYTX getting rewarded a voucher, despite the relatively low count of vouchers distributed annually. PRVs are also possible for all other drugs in the pipeline.
2) CURB906 monoclonal antibody cytotoxic conjugate for the treatment of Glioblastoma.
(10/16/2020 NIH gives a grant of license for worldwide rights)
The second license was filed near July 2020 for a novel monoclonal antibody conjugate to treat brain cancer. Glioblastomas are aggressive brain tumors with poor survival rates in children. Recent studies (e.g. s1, s2) have shown different combinations of chemo-therapy and antibody-drug conjugate (ADCs) therapeutics were effective in both mice and human models. ADCs are innovative methods that attach a cytotoxic compound (one meant to kill cancer cells) to an antibody that specifically attaches to certain cancer cell receptors, thus delivering therapies to their targets. There is great promise and lots of potential in these therapeutics. Exclusive Evaluation and Commercialization Option License Agreement with the National Cancer Institute (NCI) has been granted.
3) Metformin repurposed to treat retinal degeneration.
(2/4/2021 NIH gives a grant of license for worldwide rights)
This is probably the ace in the hole and the largest reason behind the recent stock surge. On 2/4/2021, CTYX announced they received an NIH grant for exclusive worldwide rights to adapt a diabetes drug, Metformin, to treat retinal degeneration. Not only is Metformin proven safe (it is a widely used drug to treat Type1 Diabetes since 1995), there are many studies (e.g. s1, s2, s3) that hint at its effectiveness for retinal diseases. The recently granted license not only covers pediatric retinal generation (in the form of Stargardt Disease), it covers treatment in adults as well and includes macular degeneration. This promising treatment potentially covers 2/3 of the US population (2/3 of Americans are pre-diabetic, 1/10 are diabetic, and 11 million have some form of macular degeneration; why care about diabetes? diabetes causes retinopathy).
Huge Upcoming Announcements
The announced name change is the opening of the flood gates for all upcoming news. Additional licenses, uplistings, and deals with be done under the new company name. Expect many of these announcements following FINRA approval. These are some forward-looking implications:

1. (Within 2 weeks) FINRA approval of name change to Curative Biotechnology Inc. and ticker $CURB.
2. (Within weeks of name change) Following the name change, there will be an uplisting to OTCQB. OTCQB is a tier up from Pink Sheets and must adhere to stricter management certifications, undergo annual audits, and are more stringent in their financial reporting. Connectyx is currently working to become fully reporting OTCQB; to that end, the Company appointed Jonathan D. Leinwand, PA as Legal Counsel.
3. (Within weeks of name change) Talk of multiple upcoming drugs (if the Metformin announcement was one of them, we should see at least one more).
4. (Within weeks of name change) Hints at $100M of non-dilutive funding for clinical trials.
5. (Within months of name change) Mergers, acquisitions, and partnerships with other firms for licensing and commercialization.

Downsides
Before we get ahead of ourselves and dream about retiring in 3 months while riding this into space, we gotta ground ourselves and discuss the downsides. Remember: in life, there are no solutions, only tradeoffs. There are always downsides and risks.
Risk 1) This is currently a pink sheet. That itself should make you more cautious because there is reduced regulation, more "flexible" rules, and less scrutiny/transparency.
Risk 2) High risk, high reward. If all 3 drugs flop (assuming no additional therapeutics are added) and they don't get a PRV (priority review voucher), then this company is worthless. Granted, the chances are low, but still a possibility to consider.
Risk 3) Share dilution and raising capital. Because clinical trials often require obscene amounts of capital (~$400M investment for normal drugs), there is a risk that managers might dilute the stock in order to raise money or to take profits in general. There are currently 322M outstanding shares with 1.1B authorized shares. Read the share disclosures, do the math, gauge the risks. Note that orphan drug trials are a lot less costly as well.
Risks and unknowns are certainly there. However, the upside potential is too big to ignore. Buy at pennies, sell for dollars. Do the research and take advantage of any dips that might come on Monday from 2 days of green explosions.
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TL;DR.

• You should fucking read it, because this Phoenix has a high probability of rising from ashes to become the OTC stock of the yeadecade with effortless 10x upside in the short-term.
• $CTYX will change to $CURB (Curative BioTech) soon. Business strategy: (1) bring together financial experts, veterans in big pharma, accomplished biotech researchers, and world-class grant writers to vet orphan drugs (2) make deals and obtain licenses for these drugs to help get them through clinical trials (3) take advantage of special FDA benefits for orphan drug approval (faster approval process, fee waivers, etc) and commercialize them after with longer exclusive rights.
• Finance: company has no problematic debt, clean sheets, non-dilutive funding, and a small number of outstanding shares for an OTC (322M).
• Products: 3 promising drug candidates in the pipeline within a year. Multiple exclusive license grants approved by the NIH.
• Upcoming Announcements: (1) name change (2) uplisting to $OTCQB from pink sheets (3) more non-dilutive funding (4) additional drug(s) in pipeline (5) mergers, acquisitions, and deals with other pharma companies.
• Current market cap: $50M. Upside: (1) +$100M - $300M if awarded a priority review voucher (PRV) (2) +hundreds of millions in market cap if any of the 3 promising drugs goes past phase 2 ~end of 2022 (3) +millions in speculative capital if new drugs are announced in pipeline (4) potential future merger with large pharma or uplisting to NASDAQ (other biotech companies are listed with half the number of products).

Resources
Again, these are just my thoughts. For your own research, I've linked some relevant forums, analysis, grant listings, company resources, insider profiles, and other sources. Happy digging.
Company
Company Website (new website coming soon w/ new company name)
Yahoo Finance (has all their press releases, financial summaries, and prospectives)
"Prospective" Grant Listings (all grants listed have been approved)
CTYX Financial Filings
CTYX Share Structure and Security Details
Insider Personel
CEO LinkedIn (Paul M Michaels)
CSO LinkedIn (Barry A. Ginsberg)
VP Communications (Pam Bisikirski)
Chairman of Audit Committee of Board (Michael K. Fish)
Forums / Discussions
https://stocktwits.com/symbol/CTYX (~200 followers right now)
https://investorshub.advfn.com/Connectyx-Techs-Hldg-CTYX-15134/ (warning: UI is god awful)

The complex number (2 + 5i) is a root of the quadratic equation z² - (3 + 7i)z + p +qi = 0, where p and q are real.
Find the values of p and q:

p = -8 q = 9 

By considering sum of the roots, find the second root. Why are the two roots not complex conjugates?

2 + 5i + x + yi = 3 + 7i x + yi = 1 + 2i 

Why are these two roots not complex conjugates. It's something to do with them not being real but I'm struggling to come up with it. Any help would be great.