If z = √(3)2 + i2 (i = √(-1)), then (1 + iz + z⁵ + iz⁸)⁹ is equal to

Correct option is A. -1
z=√3/2 + i/2 = cos π/6 + isin π/6 ⇒ z⁵ = cos 5π/6 + isin 5π/6 = -√3/2 + i/2
and z⁸ = cos 4π/3 + isin 4π/3 = -(1+i√3/2) ⇒ (1+iz+z⁵+iz⁸)⁹ = (1+i√3/2 -1/2 -√3/2 + 1/2 -i√3/2)⁹ = (1+i√3/2)⁹ = cos 3π + sin 3π = -1