How to do you represent the complex number, -3i, in polar form?

Reasonable question. Follow this presentation and you can answer your question.

You are familiar with the Cartesian Coordinate System (or x-y axis).

Complex numbers have two parts - real and imaginary. To picture the number a + bi, look at the point (a, b) on the Cartesian Coordinate System in which the x axis measures the real part and the y axis measures the imaginary part.

So, the complex number - 3i (= 0 - 3i) would be pictured as the point (0, -3).

In polar form, (-3, 4) is represented by (d, theta) where d is the distance from (0, 0) to (-3, 4) and theta is the positive angle less than 360 degrees from the positive side of the x axis counterclockwise to the line segment that connects (0, 0) to (-3, 4).

In polar form, the number -3 + 4i is 5 (cos theta + i sin theta),

where theta is equal to arctan (y/x) + pi = arctan (4/(-3)) + pi = arctan (-(4/3)) + pi.