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 Number Calculator
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