Answer :

Solution :

Let Z = 1 + i

Comparing with cartesian form x = 1 and y = 1

θ = tan^-1(y/x) = tan^-1(1) = $\frac{\pi }{4}$ ,

∴ r = $\sqrt{x^2+y^2}$ = $\sqrt{1^2+1^2}$ = $\sqrt{2}$

Z = re^iθ = $\sqrt{2}{e}^{i\frac{\pi }{4}}$

Zⁿ = (re^iθ)ⁿ = rⁿe^niθ

(1 + i)⁸ = ${\left(\sqrt{2}{e}^{i\frac{\pi }{4}}\right)}^8$ = 16 × e^i2π  = 16 (cos 2π + i sin 2π)

(1 + i)⁸ = 16 × 1 = 16.