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
Rewrite system of equations into form :
$\displaystyle \begin{cases}w+z=1 \\2wz-z^2-1=0 \end{cases}$
and set conditions $\displaystyle z,w \neq 0$ ,therefore :
$\displaystyle \begin{cases}w=1-z \\2wz-z^2-1=0 \end{cases}$
hence :
$\displaystyle 2(1-z)\cdot z-z^2-1=0$
Solve quadratic equation .