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

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- Mar 12th 2013, 12:51 AMcalmo11Help 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, 01:38 AMprincepsRe: Help with complex number equation
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 .