# Math Help - Complex Analysis - Proof Question

1. ## Complex Analysis - Proof Question

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

2. 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!