# Cyclic Nature of the Powers of i Worksheets

What is the Cyclic Nature of the Powers of i? If you are aware of all forms of numbers, you must know what complex numbers are. These numbers have two parts, including the real part and the imaginary part. The number that is written as a co-efficient of "i" is the imaginary part of the number. "i" in this number is the imaginary unit, and it equals to √(-1) and i^2=-1. So, what is the cyclic nature of the powers of i? When something is repetitive in nature, it is termed as cyclic. Now, if you raise "i" to large power, it will create a cyclic pattern. In this case, the powers of "i" repeat in a fixed pattern, and that is i, -1, -i, and 1.

• ### Basic Lesson

Demonstrates the concept of the powers of i. Practice problems are provided. Simplify: i5 If 5 is divided by 4, the remainder is 1 so the answer is i.

• ### Intermediate Lesson

Explores the nature of the powers of i. Practice problems are provided. Simplify: 3i6, i4, i12 If 6 is divided by 4, remainder is 2 - the value is -1; 3i6 = -3. If 4 is divided by 4, remainder is 0 - the value is 1. If 12 is divided by 4, remainder is 0 - the value is 1.

• ### Independent Practice 1

Contains 20 simplifying problems. The answers can be found below.

• ### Independent Practice 2

Features another 20 Cyclic Nature of the Powers of i problems.

• ### Homework Worksheet

12 Cyclic Nature of the Powers of i problems for students to work on at home. Example problems are provided and explained.<

• ### Topic Quiz

10 Cyclic Nature of the Powers of i problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Profound Variables

"The most powerful single idea in mathematics is the notion of a variable."

-- K. Dewdney