# How can you use trigonometric functions to simplify  27 e^( ( 5 pi)/3 i )  into a non-exponential complex number?

Euler's Formula states that ${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$ Using trigonometry, you can readily see that $x = \cos \left(\theta\right) \mathmr{and} y = \sin \left(\theta\right)$. Hence, for your question, $27 {e}^{\frac{5 \pi}{3} i} = 27 \left(\frac{1}{2} - \frac{\sqrt{3}}{2} i\right)$ .