Let z₁, z₂ and z₃ be three complex numbers on the circle |z|=1 with (z₁ )= - 4 , (z₂ )=0 and (z₃ )= 4 . If |z₁ z ₂+z₂ z ₃+z₃ z ₁ |^2= + 2 , , Z , then the value of ^2+ ^2 is :

Step-by-step solution

aligned & |z|=1 & (z₁ )=- 4 , (z₂ )=0, (z₃ )= 4 & z₁=|1| e^ - 4 = 1 2 - i 2 & z₂=1+0 i & z₃= 1 2 + i 2 & z₁ z ₂= 1-i 2 & z₂ z ₃= 1-i 2 & z₃ z ₁= (1+i)^2 2 & z₁ z ₂+z₂ z ₃+z₃ z ₁= 2 +i(1- 2 ) & |z₁ z ₂+z₂ z ₃+z₃ z ₁ |^2=5-2 2 & =5, =-2 & ^2+ ^2=29 aligned