# Imaginary Number (*i*)

How to use the imaginary number *i* to simiplify the square root of a negative number: definition, examples, and their solutions.

## Definition

√-1 is defined as the imaginary number *i*.*i* means

the radicand is (-),

which doesn't make sense in real numbers.

So the numbers with *i* are the imaginary numbers.

## Example 1: Simplify √-3

The minus sign in the radicand

becomes the *i*.

So √-3 = √3*i*.

## Example 2: Simplify √-7^{2}

Previously, you've solved this example.*n*th root - Example 4

At that time,

the answer was [not a real number]

because the radicand, -7^{2}, is (-).

Let's solve this example

by using the imaginary number *i*.

The minus sign in the radicand

becomes the *i*.

So √-7^{2} = √7^{2}*i*.

Cancel the square and the square root.

Then √7^{2}*i* = 7*i*.

Square root