Question

If $z_1$ and $z_2$ are conjugate to each other, then find $arg(-z_1{z}_2)$.

• A. $\pi$
• B. $-\pi$
• C. $\frac{\pi }{2}$
• D. $-\frac{\pi }{2}$

Answer 1

The correct option is A $\pi$

$z_1$ and $z_2$ are conjugate to each other, i.e., $z_2={\overline{z}}_1$.
Therefore, $arg(-z_1{z}_2)=arg(-z_1{\overline{z}}_1)=arg(-{\left|z_1\right|}^2)$

$=arg($Negative real number$)$
$=\pi$
Ans: A