Complex Numbers And Quadratic Equations question 41
Question: If z is a complex number, then $ z.\overline{z}=0 $ if and only if
Options:
A) $ z=0 $
B) $ Re(z)=0 $
C) $ Im(z)=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ z=x+iy,\overline{z}=x-iy $
$ \therefore $ $ z\overline{z}=0 $
Þ $ (x+iy)(x-iy)=0 $
Þ $ x^{2}+y^{2}=0 $ It is possible only when $ x $ and $ y $ both simultaneously zero i.e., $ z=0+0i=0 $
BETA
