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 coefficient 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: i^{5} If 5 is divided by 4, the remainder is 1 so the answer is i.
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Intermediate Lesson
Explores the nature of the powers of i. Practice problems are provided. Simplify: 3i^{6}, i^{4}, i^{12} If 6 is divided by 4, remainder is 2  the value is 1; 3i^{6} = 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.
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Independent Practice 1
Contains 20 simplifying problems. The answers can be found below.
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Independent Practice 2
Features another 20 Cyclic Nature of the Powers of i problems.
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Homework Worksheet
12 Cyclic Nature of the Powers of i problems for students to work on at home. Example problems are provided and explained.<
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Topic Quiz
10 Cyclic Nature of the Powers of i problems. A math scoring matrix is included.
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Profound Variables
"The most powerful single idea in mathematics is the notion
of a variable."
 K. Dewdney