1. complex numbers question

Hi,
firstly, is this the appropriate place to post questions related to complex numbers? I couldn't seem to find a better place.. so move this if its in the wrong area.
EDIT: i just realized this would probably be better in the Advanced algebra section...

ok, my question is this:
Given that z = 2 + 3i is a solution to the equation z^3 - 6z^2 + 21z -26 = 0
a) write down another complex solution of the equation.
I wrote 2 - 3i (the conjugate). is that correct?
b) Hence find a quadratic factor of the left hand side of the equation
c) Find the third solution.

I'm not sure how to do the rest of those...

2. Originally Posted by scorpion007
Hi,
firstly, is this the appropriate place to post questions related to complex numbers? I couldn't seem to find a better place.. so move this if its in the wrong area.
EDIT: i just realized this would probably be better in the Advanced algebra section...

ok, my question is this:
Given that z = 2 + 3i is a solution to the equation z^3 - 6z^2 + 21z -26 = 0
a) write down another complex solution of the equation.
I wrote 2 - 3i (the conjugate). is that correct?
The complex roots of polynomial equations with real coefficients always
occur in conjugate pairs, so yes this is right.

b) Hence find a quadratic factor of the left hand side of the equation
You have two factors of your cubic (z-(2+3i)), and (z-(2-3i)). If you multiply
these together you will get a quadratic factor of the cubic with real coefficients.
This is the quadratic factor you are looking for here.

c) Find the third solution.