Question

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

Answer 1

Use the Moivre formula.

Explanation:

The Moivre formula tells us that `e^(i*nx) = cos(nx) + isin(nx)`. You apply it to the exponential part of this complex number.

`3e^(i(3pi)/2) = 3(cos((3pi)/2) + isin((3pi)/2)) = 3(0 - i) = -3i`.