This lesson is all about taking Complex Numbers from Standard Form and transforming them in Polar Form!
We are going to see that all of the skills we’ve acquired up until now are going to help us in this lesson.
Reference Triangles and Reference Angles, the Pythagorean Theorem, SOH-CAH-TOA and the Unit Circle, Magnitude and Direction Angles for Vectors, and Polar Coordinates all come together to make something beautiful – Complex Numbers in Polar Form.
To begin, we will quickly remind ourselves how to graph a Complex Number on the Complex Plane, as well as see how to represent this number as either an ordered pair or a vector.
Complex Number in Polar Form
Next, we will learn that the Polar Form of a Complex Number is another way to represent a complex number, as Varsity Tutors accurately states, and actually simplifies our work a bit.
Then we will look at some terminology, and learn about the Modulus and Argument …. don’t worry, they’re just the Magnitude and Angle like we found when we studied Vectors, as Khan Academy states.
Phew!
And then play around with our new tools and convert Complex Numbers from Rectangular Form to Polar Form and back again.
Finally, we will see how having Complex Numbers in Polar Form actually make multiplication and division (i.e., Products and Quotients) of two complex numbers a snap!
In fact, you already know the rules needed to make this happen and you will see how awesome Complex Number in Polar Form really are.
Writing Complex Numbers in Polar Form – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.