Question

If $z_1,z_2$ and $z_3,z_4$ are 2 pairs of complex conjugate numbers, then
$arg\left(\frac{z_1}{z_4}\right)+arg\left(\frac{z_2}{z_3}\right)$ equals :

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

Answer 1

Answer: (A)

0

$z_1=\overline{z_2},z_3=\overline{z_4}$
$\Rightarrow arg(z_1)=-arg(z_2),arg(z_3)=-arg(z_4)$
Now,
$arg\left(\frac{z_1}{z_4}\right)+arg\left(\frac{z_2}{z_3}\right)$
$=arg(z_1)-arg(z_4)+arg(z_2)-arg(z_3)$
$=-arg(z_2)+arg(z_3)+arg(z_2)-arg(z_3)$
$=0$