# How can you use trigonometric functions to simplify  28 e^( ( 3 pi)/2 i )  into a non-exponential complex number?

$- 28 i$
One can use here ${e}^{i x} = \cos x + i \sin x$
Hence $28 {e}^{\frac{3 \pi}{2} i} = 28 \left(\cos \left(\frac{3 \pi}{2}\right) + i \sin \left(\frac{3 \pi}{2}\right)\right)$
or $28 \left(0 + i \left(- 1\right)\right)$ or $- 28 i$