Complex Numbers And Quadratic Equations question 424
Question: If $ z\ne 0 $ is a complex number, then
Options:
A) $ Re(z)=0\Rightarrow Im(z^{2})=0 $
B) $ Re(z^{2})=0\Rightarrow Im(z^{2})=0 $
C) $ Re(z)=0\Rightarrow Re(z^{2})=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
If $ z\ne 0 $ . Let $ z=x+iy $
Þ $ z^{2}=x^{2}-y^{2}+i(2xy) $ Re(z)= 0
Þ $ x=0 $ . Therefore $ Im(z^{2})=2xy=0 $ Thus $ Re(z)=0\Rightarrow Im(z^{2})=0 $ .
BETA
