# Math Help - [SOLVED] Complex Number Problem

1. ## [SOLVED] Complex Number Problem

Question:
Solve for z, in exact polar form, in the equation $z(z - c) = -c^2$ where c is a some positive constant.
Plot the solutions on the Argand plane.

My workings
$z(z - c) = -c^2$
$z^2 - zc = -c^2$
$z^2 = zc - c^2$

My queries:
How do I isolate the z/ do I need to?
This question asks for ploting points does that mean I need actual values?
If yes how do I get actual values out of the question?

2. Originally Posted by Evales
Question:
Solve for z, in exact polar form, in the equation $z(z - c) = -c^2$ where c is a some positive constant.
Plot the solutions on the Argand plane.

My workings
$z(z - c) = -c^2$
$z^2 - zc = -c^2$

Mr F says: ${\color{red}\Rightarrow z^2 - c z + c^2 = 0}$

Use the quadratic formula and simplify the result:

${\color{red} \Rightarrow z = \frac{c(1 \pm i \sqrt{3})}{2}}$

[snip]
..

3. Thanks a lot! I can't believe I didn't think of that