If x_n= ( 4^n )+i ( 4^n ) , then x₁ x₂ x₃ is equal to

Step-by-step solution

We have, aligned x_n & =e^i 4 n x₁ x₂ x₃ & =e^i 4 e^i 4^2 e^i 4^3 & =e^ i ( 1 4 + 1 4^2 + 1 4^3 ) =e^ i 1 / 4 1- 1 4 & =e^i 3 = 60^ +i 60^ = 1 2 + i 3 2 & = 1+i 3 2 aligned