Simplify powers of the imaginary unit

The  exercise appears under the Algebra II Math Mission. This exercise introduces and develops the arithmetic of complex numbers.

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


 * 1) Raise the imaginary unit to the given power: This problem has i, the imaginary unit, raised to a natural number. The student is expected to find the correct answer and select it from the multiple choice list.Iup1.png

Strategies
Knowledge of numerical operations and polynomial operations are encouraged to ensure success on this exercise.
 * 1) There are only four possible answers for I raised to an integer power, it will be either i, -1, -i or 1.
 * 2) Divide the power by four and a remainder of 1, 2, 3 or 0 will correspond to an answer of i, -1, -i or 1.

Real-life Applications

 * 1) Complex numbers have applications as models in non-Euclidean geometries.
 * 2) Complex numbers are used to create fractal images.
 * 3) Complex numbers are a natural extension of the real numbers.