00:03
We have the complex number 1 plus i square root of 3, and the first thing we want to do is plot this on the axes, and then they want us to turn this into polar form.
00:16
So we always plot the real part on the horizontal axis and the imaginary part on the vertical axis, and this is in the form a plus b, i.
00:29
So a is the real part, so a is one.
00:33
B is the coefficient of i in the imaginary part, so b is the square root of three.
00:38
So we're going to go to one on the real axis, and the square root of three on the imaginary axis, and there's our plot of this complex number.
00:51
Now to turn this into polar form, we want to find the radius from the origin out to the point, and we want to find the angle theta that that makes with.
01:04
The positive horizontal axis with the real axis.
01:09
So we can do this just by making our right triangle, coming down to the real axis.
01:16
The distance of the radius is going to be the absolute value of z, which is the square root of a squared, plus b squared.
01:28
So 1 squared is 1, and square of 3 squared is 3...