Complex Numbers And Quadratic Equations question 39
Question: If $ z $ is a complex number, then $ (\overline{{z^{-1}}})(\overline{z})= $
Options:
A) 1
B) -1
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ z=x+iy,\overline{z}=x-iy $ and $ {z^{-1}}=\frac{1}{x+iy} $
Þ $ (\overline{{z^{-1}}})=\frac{x+iy}{x^{2}+y^{2}} $ ;
$ \therefore $ $ (\overline{{z^{-1}}})\bar{z}=\frac{x+iy}{x^{2}+y^{2}}(x-iy)=1 $
BETA
