I have a triangle $ABC$ in a complex plane. The arrangement of vertices is in a counterclockwise direction. The coordinates of $A$,$B$,$C$ are $z_A$,$z_B$,$z_C$ respectively. It is given that length of side $AB = c, AC = b$ and $\angle BAC = \alpha$. I need to find the other sides and angles of the triangle. How do i do this with complex numbers?
I know with trigonometry using the sine and cosine rules, all the length and angles can be derived. but how to get it using complex numbers?