Given as
Z = sin π/5 + i(1 – cos π/5)
On using the formula,
sin 2θ = 2 sin θ cos θ
1 - cos 2θ = 2 sin2 θ
Therefore,
Z = 2 sin π/10 cos π/10 + i(2 sin2 π/10)
= 2 sin π/10 (cos π/10 + i sin π/10)
Thus, the polar form of sin π/5 + i(1 – cos π/5) is 2 sin π/10(cos π/10 + i sin π/10)
