Find Formula for z in Complex Quadratic Equation

[squaremeplz]

Homework Statement

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)

Homework Equations

I multiply the whole equation by z

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

=

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

=

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

using the quadratic formula

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

thanks!

The Attempt at a Solution

 

[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.