MathsGee Answers is Zero-Rated (You do not need data to access) on: Telkom | Dimension Data | Rain | MWEB
First time here? Checkout the FAQs!
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $\left|z_{1}+z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right|$ then $\arg z_{1}-\arg z_{2}$ is equal to

1) $\frac{\pi}{2}$
2) $-\pi$
3) 0
4) $-\frac{\pi}{2}$
in Mathematics by Diamond (74,746 points) | 17 views

1 Answer

0 like 0 dislike
Best answer




Let $Z_{1}=r_{1} e^{i r}, Z_{2}=r_{2} e^{i q_{2}}$
$\Rightarrow r_{1}^{2}+r_{2}^{2}+2 r_{1} r_{2}\left(Q_{1}-Q_{2}\right)=r_{1}^{2}+r_{2}^{2}+2 r_{1} r_{2}$
$\Rightarrow \cos \left(Q_{1}-Q_{2}\right)=1 \Rightarrow Q_{1}-Q_{2}=0$
$\therefore \arg \left(Z_{1}\right)-\arg \left(Z_{2}\right)=0$

by Diamond (74,746 points)

Related questions

MathsGee provides answers to subject-specific educational questions for improved outcomes.

On MathsGee Answers, you can:

1. Ask questions
2. Answer questions
3. Comment on Answers
4. Vote on Questions and Answers
5. Donate to your favourite users

Registered Members Online
MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

ZeroEd Search Engine

Other Tools

MathsGee ZOOM | eBook