Question

Express( (√3 +i )^60 )in polar form​

Answer 1

Observe that

|√3 + i| = √((√3)² + 1²) = √4 = 2

and

arg(√3 + i) = arctan(1/√3) = π/6

so that

√3 + i = 2 exp(i π/6)

By de Moivre's theorem, we get

(√3 + i)⁶⁰ = 2⁶⁰ exp(i π/6 • 60) = 2⁶⁰ exp(i 10π) = 2⁶⁰