# How do you multiply #e^(( 5 pi )/ 3 i) * e^( 3 pi/2 i ) # in trigonometric form?

##### 1 Answer

#### Explanation:

By Euler's formula:

Hence, the above becomes a FOIL problem:

Let's plug in the values, which we know from the unit circle:

Which is clearly on the unit circle! With a little thinking, we realize this is at

We can now realize that since this is an exponential, we could have used an exponential rule that we know:

Subtracting off a full rotation (

as we found trigonometrically.