00:01
The polynomial has a 0 -1 -3i.
00:04
It also has a 0 -1 plus 3i, because complex zeros never travel as 1.
00:12
They always come in pairs.
00:14
So that means our polynomial has factors x plus 2 quantity squared because of that multiplicity of 2, an x -minus 1 -3i, and x minus 1 plus 3i.
00:34
There's a trick to multiplying these complex factors, and you can just put parentheses around your x minus ones, and treat them as though they are single terms.
00:47
X plus 2 times x plus 2 is going to give me x squared plus 4x plus 4.
00:59
X minus 1 times x minus 1 is x minus 1, 1 squared minus 9 i squared because your outer and inner terms will cancel.
01:12
That gives you x squared minus 2x plus 1.
01:18
This will become plus 9.
01:21
That's because i is the imaginary unit and it's equal to the square root of negative 1...