These worksheets will give your students practice in solving equations on the powers of i.

The imaginary unit i has a really cool property about it. When you successive raise the unit to higher powers it produces a repeating pattern. In this series of worksheets we will explore that trend and help students make sense of it. The activities on these sheets will provide practice for solving various algebraic expressions demonstrating the cyclic nature of the powers of i. Both simple and complex equations are presented for the student to solve. This set contains all introductory material, practice questions, reviews, longer exercise sheets, and quizzes.

Using the property of cyclic powers of i, these worksheets show how to simplify equations that have variables and multiple powers.

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Follow the steps given to learn how to simplify this equation: i4 + i9 - i8

Cyclic Nature of the Powers of i - Worksheet 1

Simplify each equation. Example: i5 + 2i5 + i12

Worksheet 2

Simplify each equation. Example: i6 + 3i7 + i15

Review Sheet

Simplify the following equation: i5 + i12 + i6

Quiz Sheet

Simplify each equation, then check your answers and record your total score below. Example: (i4)6

Cyclic Nature of the Powers of i - Do Now

Complete the following problems, then put your answer in the "My Answer" box. Example: 5i6.2i3.4i2