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

1 Answer
Mar 25, 2018

We have to use color(red)("Euler's Identity"), that claims that

e^(ix) = cos x + i sinx.

By plugging in x= pi/2 respectively, we get :

e^(color(red)(pi/2)i) = cos color(red)(pi/2) + i sincolor(red)(pi/2) = i

I am not sure whenever you meant e^((3pi)/2i) or simply e^((3pi)/2). If you meant what you wrote, then you simply have :

e^((3pi)/2) * e^(pi/2i) = ie^((3pi)/2)

If not, then you can use some basic properties of powers in order to simply things :

e^((3pi)/2 i) * e^(pi/2i) = e^((3pi+pi)/2i) = e^(2pii)

Apply the formula again.

e^(color(red)(2pi)i) = cos color(red)(2pi) + isincolor(red)(2pi) = 1.