# Math Help - Complex number algebra question

1. ## Complex number algebra question

Hi, can someone please verify my answers to this question. Thanks heaps!!

Find all complex numbers w and z satisfying:

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

- I got the answers z = 1/3 +(or)- (√2 / 3) i and w = 2/3 + (or) - (√2 / 3)i

2. ## Re: Complex number algebra question

You are absolutely right.

Yea correct.

4. ## Re: Complex number algebra question

Multiply both sides of $\frac{1}{z}+ \frac{1}{w}= \frac{1}{wz}$ by wz to get w+ z= 1. Then w= 1- z so the second equation becomes $2wz - z^2 -1= 2(1- z)z- z^2- 1= 2z- 2z^2- z^2- 1= -3z^2+ 2z- 1 = 0$ which the same as $3z^2- 2z+ 1= 0$. Use the quadratic formula, or complete the square, to solve that for z