complex quadratic

[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

using the quadratic formula

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



is this correct?

thanks!



3. 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.