z=1/2-i√3/2 , find z^3
This complex number can be written as,
z = cos(-60) + i.sin(-60)
Using de Moivre’s formula, viz. (cos(θ) + i.sin(θ))^n = cos(n θ) + i.sin(n θ),
z^3 = (cos(-60) + i.sin(-60))^3 = cos(3*(-60)) + i.sin(3*(-60))
z^3 = cos(-180) + i.sin(-180)
z^3 = cos(360 – 180) + i.sin(360 – 180)
z^3 = cos(180) + i.sin(180)
z^3 = -1 + i.0
z^3 = -1