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