If z= 3 2 + i 2 , i= -1 , then (z²⁰¹-i )⁸ is equal to

Step-by-step solution

z = 3 2 + i 2 = e^ i /6 . z²⁰¹ = e^ i 201 /6 = e^ i 33.5 = e^ i(33 + /2) . Since e^ i 33 = e^ i = -1 , we get z²⁰¹ = -1 e^ i /2 = -i . z²⁰¹ - i = -i - i = -2i . (z²⁰¹ - i)^8 = (-2i)^8 = 2^8 i^8 = 256 1 = 256 .