1)

Let ω=eiπ/3 and a,b,c,x,y,z be non  zero complex numbers such that a+b+c=x, a+bω+cω2=y,a+bω2+cω=z

then the value of |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, ω=e12π/3,  then only integer solution exists

 Then |x|2+|y|2+|z|2|a|2+|b|2+|c|2=3