# Imaginary Number Calculator

Imaginary Number Calculator helps to find the square root of an imaginary number. The square roots of negative numbers that do not have a definite value are known as imaginary numbers.

## What is an Imaginary Number Calculator?

Imaginary Number Calculator is used to determine the square root of a pure imaginary number. We express an imaginary number by using the imaginary unit called iota or "i". To use the * Imaginary Number Calculator, *input the imaginary number in the given input box.

### Imaginary Number Calculator

## How to Use Imaginary Number Calculator?

Follow the steps given below to find the square root of an imaginary number using the online Imaginary Number Calculator

**Step 1:**Go to Cuemath's online imaginary number calculator.**Step 2:**Enter a negative number in the input box of the imaginary number calculator.**Step 3:**Click on the**"Calculate"**button to find the square root of the imaginary number.**Step 4:**Click on the**"Reset"**button to clear the field and enter new values

## How Does Imaginary Number Calculator Work?

When we square an imaginary number, it results in a negative number. A pure imaginary number is in the form of bi, where b is a non-zero real number. Further, an imaginary number can be thought of as the product of a real number and iota (i). Suppose we have a negative number -x. The square root is √−x. This value remains undefined. We represent this number as i√x. Thus, i will be equal to √−1. If we take the square of i we will get -1 (i × i = √−1 × √−1 = -1).

The sum of a real number and an imaginary number is known as a complex number. It is represented as z = a + bi. Here, a is the real part which is written as Re(z). Similarly, b is the imaginary part written as Im(z).

To find the square root of a pure imaginary number we first express the number as i√x. Then we use the method of simplifying radicals to find the square root.

## Solved Examples on Imaginary Numbers

**Example 1:** What is the square root of the number -49 and verify it using the online Imaginary number calculator?

**Solution:**

√-49 = i√49.

On simplifying the radical, we get

i√49 = i√(7 × 7) = 7i

Thus, √-49 = 7i.

**Example 2:** What is the square root of the number -24 and verify it using the online Imaginary number calculator?

**Solution:**

√-24 = i√24.

On simplifying the radical, we get

i√24 = i√(4 × 6) = 2 i √6

Thus, √-24 = 2 i √6.

Now, you can try the Imaginary number calculator to find the square root of the following numbers:

- -500
- -36

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