# How can you use trigonometric functions to simplify  2 e^( ( 17 pi)/12 i )  into a non-exponential complex number?

$2 \left[\cos \left(\frac{17 \pi}{12}\right) + i \sin \left(\frac{17 \pi}{12}\right)\right]$
Use Euler's formula for complex numbers ${e}^{i t} = \cos t + i \sin t$
Accordingly $2 {e}^{\frac{17 \pi i}{12}} = 2 \left[\cos \left(\frac{17 \pi}{12}\right) + i \sin \left(\frac{17 \pi}{12}\right)\right]$