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

The Moivre formula tells us that ${e}^{i \cdot n x} = \cos \left(n x\right) + i \sin \left(n x\right)$. You apply it to the exponential part of this complex number.
$3 {e}^{i \frac{3 \pi}{2}} = 3 \left(\cos \left(\frac{3 \pi}{2}\right) + i \sin \left(\frac{3 \pi}{2}\right)\right) = 3 \left(0 - i\right) = - 3 i$.