# How can you use trigonometric functions to simplify  7 e^( ( 3 pi)/8 i )  into a non-exponential complex number?

$7 \cos \left(\frac{3 \pi}{8}\right) + 7 i \sin \left(\frac{3 \pi}{8}\right) =$
$\frac{7}{2} \left(\sqrt{2 - \sqrt{2}} + i \sqrt{2 + \sqrt{2}}\right)$
Use definition of ${e}^{i \theta}$ and half angles formulas.