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.