How do I express sin(e^i) in terms of z = x + yi with x,y in R.
I say that e^i = cos1 + i*sin1 (since e^z = e^x(cosy + i*siny).
Then sin(cos1 + i*sin1) = [e^(i*(cos1 + i*sin1)) - e^(-i*(cos1 + i*sin1))]/2i, which equals (e^(i*cos1 - sin1) - e^(-i*cos1 + sin1))/2i. How do I write this in the form x + yi?
Thanks for your help in advance.