# Polynomial Complex Numbers

• Oct 1st 2009, 02:47 PM
dnm40
Polynomial Complex Numbers
Hi! First off, great forum, used it as a guide for quite some time :)

So, got a problem, polynomials isnt my strongest suit i guess, so here goes:

Find all the complex solutions to the equation:
z^4 − z^2 + 3 = 0

Then factorize z^4 − z^2 + 3, first in complex first grade polynomials, then in second grade?
• Oct 1st 2009, 02:57 PM
Matt Westwood
Quote:

Originally Posted by dnm40
Hi! First off, great forum, used it as a guide for quite some time :)

So, got a problem, polynomials isnt my strongest suit i guess, so here goes:

Find all the complex solutions to the equation:
z^4 − z^2 + 3 = 0

Then factorize z^4 − z^2 + 3, first in complex first grade polynomials, then in second grade?

Set $z^2 = w$, say. Then you have a quadratic in w.

This will give you an equation where $z^2$ equals either of two values, as given by the standard way of solving a quadratic. Which gives you 2 values of z for each.