00:02
I'm going to jump right into the synthetic division, and not everybody is very good at synthetic division, but it's actually fun for me to examine imaginary numbers with this.
00:16
So 4, 5, 94, 125, and negative 50.
00:25
And if that really is a zero, then i'll get a remainder of zero.
00:30
So let's see what happens.
00:31
You bring the four down and you multiply by what's in the box well that's negative 20 i now adding straight down you cannot combine five with negative 20 i so leave it separated so five times negative 25 is negative sorry i said that five times negative 25 with an i there but then a negative five times negative 20 is a positive 100 i squared makes it a negative 100 so as i add straight down minus 100 will be negative 6.
01:06
And then as i go to the next one, negative 6 times negative 5 is 30.
01:13
I, and then negative 25 times negative 5 is positive 125.
01:21
I squared makes it a negative.
01:24
So now we're left with 30i because these cancel.
01:28
Well, 30 times negative 5 is negative 150, d, but i squared changes the side of it.
01:36
And look at that.
01:37
So now the next 0 would have to be its complex conjugate.
01:44
So positive 5i, check out this magic.
01:47
Again, it'll work because you'll get a remainder of 0...