00:01
Numbers, two or three numbers we want to find the roots of.
00:04
Let me go ahead and get those written down.
00:06
That's an i, and then two square roots of three minus two i, and that's to the one -fourth.
00:13
We're going to do all these at the same time, because they were all going to be done the same way, and i might not get all the final answers there, but you'll be able to get those.
00:21
So here we go.
00:22
For the first one, each one we're going to draw a little graph.
00:24
So see, that's going to be over here at this point here.
00:29
This one is going to be negative 8i, which would be about right here, and then this one's going to be in the fourth quadrant, so be about right here.
00:39
Now the reason we want to do this is we want to get it in polar form, which is going to be r cis theta.
00:44
The first two are really quite easy.
00:47
We're going to have here the r is going to be simply at 256 because because we're going that far, 256 cis, and because we're on this axis, we're looking at 0 degrees.
00:58
Here, we're going to have the r value is going to be 8, because we're looking at a distance of 8 cis.
01:04
That's going to be at 270 degrees.
01:08
Here, we have a little more work.
01:09
Our r is going to be the square root of 2 square roots of 3 squared plus negative 2 squared.
01:17
So it's going to be the square root of 4 times 3, which is going to be 4 times 3 plus 4, or square root of 16, which is 4.
01:28
And my theta, we're going to go inverse tangent of 2 over 2 square roots of 3.
01:35
And i know that that's going to give me a reference angle.
01:39
I never can remember this one for some reason.
01:42
An inverse tangent of 1 divided by the square root of 3, 30 degrees...