Complex number polar form intuition

The  exercise appears under the Precalculus Math Mission. This exercise plots complex numbers on the complex plane and explores the connection between rectangular and polar forms of complex numbers.

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


 * 1) Plot the point on the plane: This problem provides a complex number given in rectangular coordinate form. The student is expected to find the radius and angle that would make the complex number in a polar view.Cnpfi1.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) 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.