z=cos‌θ+i‌sin‌θ=eiθ‌‌‌‌‌ [in Euler's form] Using Demoivre theorem z2=cos‌2‌θ+i‌sin‌2‌θ z3=cos‌3‌θ+i‌sin‌3‌θ Now, according to the question
15
∑
m=1
Im(z2m−1) ⇒ Imaginary part of (z+z3+z5+...+z29) ⇒ sin‌θ+sin‌3‌θ+sin‌5‌θ+...sin‌29‌θ) ⇒