00:01
For this problem, we are shown a figure which has one of the fourth roots of a complex number.
00:08
The first part we want to answer how many roots are not shown, and for the second part we want to describe the other roots.
00:17
So first of all, we can see that we have a root.
00:19
We can see that its magnitude is outside of the unit circle, this first thick line would be at radius 1 there.
00:30
And we can see that it is at, currently it's at an angle of 30 degrees.
00:36
So since this is a fourth root, we know that its theta is going to be equal to our, i guess we could say theta k, is going to equal our original theta over four.
00:56
We'll assume for our purposes here that this is going to be k equals zero.
01:00
It doesn't really matter which k this is.
01:05
Then, from that, we would be able to know that our original theta is going to end up being 30 times four.
01:16
So our original theta would end up being 120...