Complex Numbers And Quadratic Equations question 57
Question: If $ z_1 $ and $ z_2 $ are any two complex numbers then $ |z_1+z_2{{|}^{2}} $ $ +|z_1-z_2{{|}^{2}} $ is equal to [MP PET 1993; RPET 1997]
Options:
A) $ 2|z_1{{|}^{2}}|z_2{{|}^{2}} $
B) $ 2|z_1{{|}^{2}}+2|z_2{{|}^{2}} $
C) $ |z_1{{|}^{2}}+|z_2{{|}^{2}} $
D) $ 2|z_1||z_2| $
Show Answer
Answer:
Correct Answer: B
Solution:
$ |z_1+z_2{{|}^{2}}+|z_1-z_2{{|}^{2}} $ $ ={{(x_1+x_2)}^{2}}+{{(y_1+y_2)}^{2}}+{{(x_1-x_2)}^{2}}+{{(y_1-y_2)}^{2}} $ $ =2(x_1^{2})+2(y_1^{2})+2(x_2^{2})+2(y_2^{2})=2|z_1{{|}^{2}}+2|z_2{{|}^{2}} $
BETA
