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.](https://ximpledu.com/en-us/imaginary-number-i/imaginary-number-i-01-02.png "Imaginary Number (i): Definition, Formula")
√-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]](https://ximpledu.com/en-us/imaginary-number-i/imaginary-number-i-02-02.png "Imaginary Number (i): Example 1, Solution")
The minus sign in the radicand
becomes the i.
So √-3 = √3i.
Example 2: Simplify √-72
![Simplify the given expression. Square root [-7^2]](https://ximpledu.com/en-us/imaginary-number-i/imaginary-number-i-03-02.png "Imaginary Number (i): Example 2, Solution")
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
