# How can you use trigonometric functions to simplify  23 e^( ( 2 pi)/3 i )  into a non-exponential complex number?

-11.5 + i 11.5 sqrt3)
The polar form of a complex number (x, y) = x + i y is r ${e}^{i \theta}$ = r (cos($\theta$) + i sin ($\theta$)). Here, r = 23 $\mathmr{and} \theta$ = 2$\pi$/3. cos ($2 \pi$/3) = cos ($\pi - \frac{\pi}{3}$) = - cos ($\frac{\pi}{3}$) and sin ($2 \pi$/3) = sins ($\pi - \frac{\pi}{3}$) = sin ($\frac{\pi}{3}$).