Equivalent forms of expressions with complex numbers

The  exercise appears under the Precalculus Math Mission. This exercise practices factoring and the distributive property as it relates to complex numbers.

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


 * 1) Find which expressions are the same: This problem provides a complex expression and several other expressions below it. The student is asked to select all of the options that are equivalent in form to the initial expression.Efoewcn1.png

Strategies
Knowledge of factoring and the distributive property are encouraged to ensure success on this exercise.
 * 1) This problem can be performed accurately by multiplying out the expressions below and seeing which match correctly.
 * 2) Factoring techniques, especially factoring difference of squares, can increase efficiency on this exercise.

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.