# Help with complex number equation

• Mar 12th 2013, 01:51 AM
calmo11
Help with complex number equation
The Question is:
Find all complex numbers 'w' and 'z' satisfying:

(1/w)+(1/z)=(1/wz) and (2wz)-(z^2)-1=0

Any help at all would be very muchly appreciated
• Mar 12th 2013, 02:38 AM
princeps
Re: Help with complex number equation
Rewrite system of equations into form :

$\begin{cases}w+z=1 \\2wz-z^2-1=0 \end{cases}$

and set conditions $z,w \neq 0$ ,therefore :

$\begin{cases}w=1-z \\2wz-z^2-1=0 \end{cases}$

hence :

$2(1-z)\cdot z-z^2-1=0$