Question

Let $z$ and $\omega$ are two non-zero complex numbers such that $|z|=|\omega |$ and $argz+arg\omega =\pi$, then $z$ equal to

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

Answer 1

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

$w=|w|e^{i\theta }$
$=|w|[cos\theta +isin\theta ]$
$z=|w|e^{i(\pi -\theta )}$
$=|w|[-cos\theta +isin\theta ]$
$=-|w|[cos\theta -isin\theta ]$
$=-\overline{w}$