Complex Numbers And Quadratic Equations question 631
Question: If z is a complex number such that $ z+|z|=8+12i, $ then the value of $ |z^{2}| $ is equal to
Options:
A) 228
B) 144
C) 121
D) 169
Show Answer
Answer:
Correct Answer: D
Solution:
$ z+|z|=8+12i $
$ \Rightarrow x+iy+\sqrt{x^{2}+y^{2}}=8+12i $
$ \Rightarrow x+\sqrt{x^{2}+y^{2}}=8 $ …(i) & $ y=12 $ …(ii) $ (x=-5) $ So, $ z=-5+12i $
$ \Rightarrow |z|=\sqrt{25+144}=13 $
$ \Rightarrow |z^{2}|=|z{{|}^{2}}=169 $
BETA
