So here again I wrote down this formula we just found.

If W is of the form rho e to the I Phi, then the nth roots of

W can be found with this formula, for these n values of k.

So let's find the square root of 4i as an example.

So first of all 4i,

we need to bring that into this form, in the form rho e to the I phi.

So we have to figure out what's rho, what's phi.

4i is 4 times instead of i we can write e to the i pi

over 2 we discovered that during the last lecture.

And so in other words, this row is 4.

And phi and a possibility for the angle phi pi over 2, and

we wanted to take this square root of the second root.

So n is 2.

So now we have everything we need to plug in this formula.

So we find 4i to the one-half is equal to

the square root of 4, times e to the i.

Now we need to take phi and divide it by n.

Phi is pi over 2, divided by n.

That gives me pi over 4.

Plus, 2 k pi over n.

We'll just write that down.

2 k pi over 2 because my n is 2.

So here's the complete formula, and we need to plug in k = 0, and then k = 1.

So we get two separate solutions.

For k = 0, this whole second term 2 k pi over 2 which is not there.

And so, we find square root of 4 which is 2 times e to the i, pi over 4.

That's one of my two square roots, and when k's equal to 1,

2k pi over 2 becomes 2 pi over 2 which is pi.

So I get 2 times either the i pi over 4 plus pi, but

remember what e to the i pi equals?

Pi is a 180 degree angle.

E to the i pi, is this number right here.

That forms a 180 degree angle.