Complex Numbers And Quadratic Equations question 47

Question: $ (z+a)(\bar{z}+a) $ , where $ a $ is real, is equivalent to

Options:

A) $ |z-a| $

B) $ z^{2}+a^{2} $

C) $ |z+a{{|}^{2}} $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

As we know if a is real, then $ a=\overline{a} $ \ $ (z+a)(\overline{z}+a)=(z+a)(\overline{z}+\overline{a})=(z+a)(\overline{z+a}) $ $ =|z+a{{|}^{2}} $