Dividing Complex Numbers Calculator

Complex numbers are numbers that are a combination of a real component and an imaginary component.

What is Dividing Complex Numbers Calculator?

'Cuemath's Dividing Complex Numbers Calculator' is an online tool that calculates the division of two given complex numbers. Cuemath's online Dividing Complex Numbers Calculator helps you to calculate the division of two given complex numbers.

NOTE: Please enter the values up to 3 digits only.

How to Use Dividing Complex Numbers Calculator?

Please follow the steps below on how to use the calculator:

• Step 1: Enter the value of complex numbers 1 and 2 in the given input boxes.
• Step 2: Click on the "Divide" button to divide the two given complex numbers
• Step 3: Click on the "Reset" button to clear the fields and enter new values.

How to Find Dividing Complex Numbers Calculator?

The number of the form z=a+ib, where a is called the real part and b is called the imaginary part.

Let x = a + ib, y = c + id

Please follow the steps below on how to divide the complex numbers:

• Step1: Calculate the conjugate of the complex number that is at the denominator of the fraction.
• Step1: Multiply the conjugate with the numerator and the denominator of the complex fraction.
• Step3: Apply the algebraic identity (c + d)(c − d) = c² − d² in the denominator and substitute i² = −1
• Step4: Apply the distributive property in the numerator and simplify.

Let us see an example to understand briefly.

Solved Example:

Divide the given complex numbers x = 3 + 4i and y = 6 + 3i 

Solution:

Given: x = 3 + 4i and y = 6 + 3i

x / y = 3 + 4i / 6 + 3i

=\(\frac{(3 + 4i)}{(6 + 3i)} × \frac{(6 - 3i)}{(6 - 3i)}\)                   

\(= \frac{(3 + 4i)×(6 + 3i)}{(6 +3i)×(6-3i)}\)

= 0.67 + ((-0.33)i)

Similarly, you can use the calculator to divide the given complex values:

• z1 = 5 + 12i, z2 = 12 + 5i

• z1 = 3 + 6i, z2 = 1 + 2i