let z = r(cosθ+i sinθ) and it is given that z¹⁵ = 1  =>  r¹⁵(cosθ+i sinθ)¹⁵ = 1

or r¹⁵(cos15θ+i sin15θ) = 1+0i                   (Here we use Demoivre's theorem)

on comparison we get sin 15θ = 0 => 15θ = nπ          here n is an integer

for n = -7 to +7 we will get 15 answers for which θ will lie between -π/2 to +π/2