# Complex Analysis - Proof Question

• Jun 5th 2011, 03:17 PM
essedra
Complex Analysis - Proof Question
Show that sin(z+w) = sinz.cosw + cosz.sinw for all z, w that are complex numbers.
• Jun 5th 2011, 03:47 PM
Plato
Quote:

Originally Posted by essedra
Show that sin(z+w) = sinz.cosw + cosz.sinw for all z, w that are complex numbers.

Surely you know that:
$\sin(z)=\frac{1}{2i}\left(e^{iz}-e^{-iz}\right)$ & $~\cos(w)=\frac{1}{2}\left(e^{iw}+e^{-iw}\right).$
Now go for it!