Multiplying and dividing complex numbers in polar form

The  exercise appears under the Precalculus Math Mission. This exercise continues exploration of multiplying and dividing complex numbers, as well as their representation on the complex plane.

Types of Problems
There is one type of problem in this exercise:


 * 1) Plot the product or quotient of the complex numbers: This problem describes an arithmetical expression with multiplying or dividing complex numbers. The student is expected to find the result and plot it on the complex plane in polar form.Madcnipf1.png

Strategies
Knowledge of the polar form of a complex number is encouraged to ensure success on this exercise.
 * 1) This problem requires a student to find the appropriate radius and angle to make a complex number.
 * 2) The radius is the magnitude of the complex number and the angle is the arctan(y/x).
 * 3) To multiply or divide complex numbers, multiply or divide the magnitudes, then add or subtract the arguments.
 * 4) This problem should always be performed correctly because the answer does not need to be submitted until it is moved to the correct place.

Real-life Applications

 * 1) Imaginary numbers are used in chaos theory for predicting chaotic situations, like earthquakes and stock markets.
 * 2) Imaginary numbers can be used to model geometry on the Cartesian plane.
 * 3) The complex plane representation of complex numbers can be used to better understand polar coordinates.