Complex Numbers And Quadratic Equations question 59
Question: If $ z $ is a complex number, then which of the following is not true [MP PET 1987]
Options:
A) $ |z^{2}|=|z{{|}^{2}} $
B) $ |z^{2}|=|\bar{z}{{|}^{2}} $
C) $ z=\bar{z} $
D) $ {{\bar{z}}^{2}}={{\bar{z}}^{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
L.H.S.= $ |z^{2}|=|{{(x+iy)}^{2}}| $ $ =|x^{2}-y^{2}+2ixy|=\sqrt{{{(x^{2}-y^{2})}^{2}}+{{(2xy)}^{2}}} $ $ =\sqrt{{{( x^{2}+y^{2} )}^{2}}} $ …….(i) R.H.S. $ =|z{{|}^{2}}=|x+iy{{|}^{2}}=\sqrt{{{(x^{2}+y^{2})}^{2}}} $ $ =x^{2}+y^{2} $ ??(ii) Therefore $ |z^{2}|=|z{{|}^{2}} $ (b) True (c) False (since $ z\ne \overline{z} $ ).
BETA
