How do you use DeMoivre's theorem to simplify (5(cos(pi/9)+isin(pi/9)))^3?

1 Answer
Aug 6, 2016

=125(1/2+ (sqrt(3))/2i)

Could also write as 125e^((ipi)/3) using Euler's formula if you so desired.

Explanation:

De Moivre's theorem states that for complex number

z = r(costheta + isintheta)

z^n = r^n(cosntheta + isinntheta)

So here,

z = 5(cos(pi/9) + isin(pi/9))

z^3 = 5^3(cos(pi/3) + isin(pi/3))

=125(1/2+ (sqrt(3))/2i)