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Complex Zeros

First, we need to do a little reviewing of complex numbers:

Remember that a complex number is a guy of the form

a + bi where i = sqrt( -1 ) and if i = sqrt( -1 ) then i^2 = -1

We ran into these when we were solving quadratics.

Let's do a couple:

Solve  x^2 + x + 1 = 0

It doesn't factor, so we hit it with

The Quadranator!

x = -1 +/- sqrt( 1^2 - 4 ( 1 ) ( 1 ) ) / ( 2 ( 1 ) ) = -1 +/- sqrt( -3 ) / 2 = -1 +/- sqrt( 3 ) i / 2

{ ( -1/2 ) - ( sqrt( 3 )/2 ) i , ( -1/2 ) + ( sqrt( 3 )/2 ) i }
Remember that these are called complex conjugates!a - bi and a + bi

*When you are solving these,
the complex guys ALWAYS occur in conjugate pairs!