Bababa ba?

This was bothering me since 12noon, and it was already 10:30pm when I finally discovered how to answer it. Para lang mapakawalan ko ito, isusulat ko rito ang problema at ang sagot. XD

Show that sin(x+iy) = sinxcoshy+icosxsinhy
Given sinz = [e^(iz) - e(-iz)] / 2i and cosz = [e^(iz) + e(-iz)]

Proof:
a. sin(x+iy) = sinxcosiy+cosxsiniy (by trig identity)
b. cosiy=coshy (by given, definition of hyperbolic cosine)
c. siniy=isinhy (by given, definition of hyperbolic sine)
d. sin(x+iy) = sinxcoshy+icosxsinhy (by substitution, a, b) QED