Complex Numbers And Quadratic Equations question 144
Question: If $ z_1,z_2 $ and $ z_3,z_4 $ are two pairs of conjugate complex numbers, then $ arg( \frac{z_1}{z_4} )+arg( \frac{z_2}{z_3} ) $ equals
Options:
A) 0
B) $ \frac{\pi }{2} $
C) $ \frac{3\pi }{2} $
D) $ \pi $
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ z_2={{\overline{z}}_1} $ and $ z_4={{\overline{z}}_3} $ Therefore $ z_1z_2=|z_1{{|}^{2}} $ and $ z_3z_4=|z_3{{|}^{2}} $ Now $ arg( \frac{z_1}{z_4} )+arg( \frac{z_2}{z_3} )=arg( \frac{z_1z_2}{z_4z_3} ) $ $ =arg( \frac{|z_1{{|}^{2}}}{|z_3{{|}^{2}}} )=arg( {{| \frac{z_1}{z_3} |}^{2}} ) $ = 0 ( $ \because $ Argument of positive real number is zero).
BETA
