Imaginary Number (i)

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

Square root[-1] is defined as the imaginary number i.

-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

Simplify the given expression. Square root [-3]

The minus sign in the radicand
becomes the i.

So √-3 = √3i.

Example 2: Simplify √-72

Simplify the given expression. Square root [-7^2]

Previously, you've solved this example.

nth root - Example 4

At that time,
the answer was [not a real number]
because the radicand, -72, is (-).

Let's solve this example
by using the imaginary number i.

The minus sign in the radicand
becomes the i.

So √-72 = √72i.

Cancel the square and the square root.

Then √72i = 7i.

Square root