How to prove this

Question

(e^(2^-1 i3pi) - e^-(2^-1 i3pi))/(2i) = -1

if you could show me this that would be really great

btw e is eulers number
i = imaginary number sqrt -1
and pi = 3.14...

THANKS!!!

Answer 1

One definition of sin x is
sinx = (e^ix - e^-ix)/2i

That means that your expression is
sin (3 pi/2)

The sine of that angle is -1