Question

Let z & w be two non zero complex numbers such that $|z|=|w|$ and $Argz+Argw=\pi$, then z equals

• A. w
• B. -w
• C. $\overline{w}$
• D. $-\overline{w}$

Answer 1

The correct option is D $-\overline{w}$

Let
$w=cos\theta +isin\theta$

$\overline{w}=cos\theta -isin\theta$

Now $arg\left(z\right)=\pi -arg\left(w\right)$

$\therefore z=cos(\pi -\theta )+isin(\pi -\theta )$

$=-cos\left(\theta \right)+isin\left(\theta \right)$

$=-\overline{w}$