Powers of complex numbers

The  exercise appears under the Precalculus Math Mission. This exercise plots powers of complex numbers on the 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 power of the complex number: This problem provides a complex number raised to an integer power. The student is expected to find the result of the expression and plot it on the complex plane.Pocn1.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) The power of a complex number is the power of it's magnitude and the multiple of it's argument.
 * 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.