Question

Use DeMoivre’s Theorem to find
[2(cosπ/10+ i sinπ/10)]^5in standard form.
a) Identify the real part.
b)identify the imaginary part.

Answer 1

z=r(cos(x)+i sin(x)) then
z^n=r^n(cos(nx)+isin(nx))

Answer 2

So
32(cos( pi/2)+isin(pi/2))=32(0+i(1))=0+32i
The real part is 0 and the imaginary part is 32i