Modular Argument!

Algebra Level 4

If $|a|=|b|^{'}$ and $arg(\frac{a}{b})$ $=$ $\pi$ , then what is the value of $a+b$ ?

Note - $a$ and $b$ are complex numbers !!!!!

-1

e^{e}

e

\infty

e^{\pi}

e^{i}

1 0

2 solutions

Karan Shekhawat
Apr 14, 2015

It must be Level-1 or 2 (max) Problem....

Gagan Raj
Apr 14, 2015

Given , $|a|=|b|$ and $arg(\frac{a}{b})=\pi$

$arg(a)-arg(b)=\pi$

$arg(a)=\pi+arg(b)$

If , $b=re^{i\theta}$

$a=re^{i(\pi+\theta)}$

$a=re^{i\pi}.e^{i\theta}$

$a=-re^{i\theta}$

$a=-b$

$a+b=0$

Hence , the answer is $0$ .