1. Sep 8, 2009

### squaremeplz

1. The problem statement, all variables and given/known data

consider

$$a*z - b*conj(z) + c = 0$$

where a,b,c are unknown complex constants.

find a formula for z in terms of a, b, c

answer should be in the form "z = ..." where the ... does not contain any z or conj(z)

2. Relevant equations

I multiply the whole equation by z

$$z*(a*z - b*conj(z) + c) = 0$$

=

$$a*z^2 - b*z^2 + c*z) = 0$$

=

$$(a - b)*z^2 + c*z = 0$$

$$z = \frac {-c \frac {+}{-} \sqrt{c^2}}{2*(a-b)}$$

is this correct?

thanks!

3. The attempt at a solution

2. Sep 8, 2009

### gabbagabbahey

No, $z\overline{z}=|z|^2\neq z^2$ in general.

Instead, take the complex conjugate of both sides of your original equation. That will give you two equations and two unknowns ($z$ and $\overline{z}$) which you should know how to solve.