Question

If $(z_1,z_2)$ and $(z_3,z_4)$ are two pairs of non zero conjugate complex numbers then
$arg\left(\frac{z_1}{z_3}\right)+arg\left(\frac{z_2}{z_4}\right)$ can be

• A. 0
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is A 0

${\overline{z}}_1=z_2$
${\overline{z}}_3=z_4$
$arg\left(\frac{z_1}{z_3}\right)+arg\left(\frac{z_2}{z_4}\right)=arg\left(\frac{z_1{z}_2}{z_3{z}_4}\right)=arg\left(\frac{z_1{\overline{z}}_1}{z_3{\overline{z}}_3}\right)=0$