00:01
In this video, we want to evaluate the power of a complex number using domo's theorem.
00:09
Our complex number is radical 3 minus i.
00:13
This is in rectangular form a plus b, i, where a is our real part, positive radical 3, and b is our imaginary part, negative 1.
00:23
That point in green is about here in the complex, rectangular complex number point.
00:31
So to figure out how to raise this to the sixth power, it's best if we write this in its trigonometric form so that we can use the mov's theorem, which means we need to figure out the radius and the angle theta.
00:45
Using the pythagorean theorem and the values of a and b, root 3 and negative 1, we can determine that our radius is positive 2.
00:58
So that's radical 3 squared plus negative 1 squared equals the radius squared.
01:05
So that's a positive 2 for our radius.
01:10
And to figure out our angle, we can use trigonometry or recognize actually that we have a special right triangle that we're dealing with.
01:18
So the special right triangle that we're working with is a 3060 -90 triangle.
01:23
In this triangle, let's just draw one as a reference.
01:30
On our unit circle, this is a 30 -degree angle...
