# complex numbers question

• Oct 14th 2006, 07:36 PM
scorpion007
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...
• Oct 14th 2006, 11:00 PM
CaptainBlack
Quote:

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.

Quote:

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.

Quote:

c) Find the third solution.