Discussion Forum



1)

Let $ \omega = e^{i \pi/3}$ and a,b,c,x,y,z be non  zero complex numbers such that a+b+c=x, $a+b \omega+c\omega^{2}=y, a+b \omega^{2}+c \omega =z$

then the value of $\frac{|x|^{2}+|y|^{2}+|z|^{2}}{|a|^{2}+|b|^{2}+|c|^{2}}$ is 


A) 3

B) 5

C) 4

D) 6

Answer:

Option A

Explanation:

 Here, $\omega= e^{12 \pi/3}$,  then only integer solution exists

 Then $\frac{|x|^{2}+|y|^{2}+|z|^{2}}{|a|^{2}+|b|^{2}+|c|^{2}}$=3