Complex Numbers And Quadratic Equations question 76
Question: $ | \frac{1}{2}(z_1+z_2)+\sqrt{z_1z_2} |+| \frac{1}{2}(z_1+z_2)-\sqrt{z_1z_2} | $ =
Options:
A) $ |z_1+z_2| $
B) $ |z_1-z_2| $
C) $ |z_1+z_2| $
D) $ |z_1|-|z_2| $
Show Answer
Answer:
Correct Answer: C
Solution:
R.H.S = $ \frac{1}{2}|{{(\sqrt{z_1}+\sqrt{z_2})}^{2}}|+\frac{1}{2}|{{(\sqrt{z_1}-\sqrt{z_2})}^{2}}| $ $ =\frac{1}{2}|\sqrt{z_1}+\sqrt{z_2}{{|}^{2}}+\frac{1}{2}|\sqrt{z_1}-\sqrt{z_2}{{|}^{2}} $ $ {\because |z^{2}|=|z{{|}^{2}}} $ $ =\frac{1}{2}2[|\sqrt{z_1}{{|}^{2}}+|\sqrt{z_2}{{|}^{2}}]=|z_1|+|z_2| $
BETA
