Simplify: i^{45}. A. 1 B. i C. -1 D. -i

Question:

Simplify: {eq}i^{45}. {/eq}

A. 1

B. i

C. -1

D. -i

Imaginary Numbers

Imaginary numbers are used in complex maths. In particular, the imaginary number i is defined as:

$$i^2=-1 $$


Due to this, the imaginary number i follows a pattern when it comes to its powers.

Answer and Explanation:

The powers of the imaginary number i follow a clear pattern. If the power is even, the answer is -1. And, if the power is odd, the answer is again i. As 45 is an odd number, the correct option is B.


Learn more about this topic:

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What is an Imaginary Number?

from Math 101: College Algebra

Chapter 5 / Lesson 1
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