# 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**.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

Get access to this video and our entire Q&A library

#### Related to this Question

Which quadrant should the graph of -4 - 9i be...

What is a pure imaginary number?

How do you simplify imaginary numbers?

Simplify in terms of i. \sqrt{-121}

Simplify: i^{-10} How exactly do I solve...

Simplify the number using the imaginary unit i....

write the expression in the form bi, where b is...

Compute e^{z} in the form x + iy and \left | e^{z}...

Is i^2 = -1?

How do you find the absolute value of imaginary...

Evaluate the following powers of i. { a) i^8...

How do you write imaginary numbers in standard...

#### Explore our homework questions and answers library

Browse
by subject