Complex Numbers And Quadratic Equations question 40
Question: If $ z $ is a complex number such that $ z^{2}={{(\bar{z})}^{2}}, $ then
Options:
A) $ z $ is purely real
B) $ z $ is purely imaginary
C) Either $ z $ is purely real or purely imaginary
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ z=x+iy $ , then its conjugate $ \overline{z}=x-iy $ Given that $ z^{2}={{(\overline{z})}^{2}} $
Þ $ x^{2}-y^{2}+2ixy=x^{2}-y^{2}-2ixy $
Þ $ 4ixy=0 $ If $ x\ne 0 $ then $ y=0 $ and if $ y\ne 0 $ then $ x=0 $
BETA
