Question

Dengan memakai bentuk kutub hitunglah: (1+i)^5

Answer 1

(1+i)⁵
z = 1+i
n = 5
r = √(1²+1²) = √2
θ = arctan (1/1)
θ = arctan 1
θ = 45°

z^n = r^n (cos nθ + i sin nθ)
(1+i)⁵ = (√2)⁵ (cos 5x45° + i sin 5x45°)
         = 4√2 (cos 225° + i sin 225°)
         = 4√2 (-√2/2 + -√2/2 i)
         = -4 - 4i