Complex Number Division Calculator

Complex Number Division Calculator calculator can be used for dividing two complex numbers and displaying the result in both rectangular and polar forms.

Input Parameters

Real part of first complex number (a)

Imaginary part of first complex number (b)

Real part of second complex number (c)

Imaginary part of second complex number (d)

Calculation Results

Calculation Formula

The division of two complex numbers (a + bi) / (c + di) is calculated as:

(ac + bd) + (bc - ad)i / (c² + d²)

Where:
a = real part of the first complex number
b = imaginary part of the first complex number
c = real part of the second complex number
d = imaginary part of the second complex number

Result

Rectangular Form: -

Polar Form: -

Complex Number Division Calculator Calculator Usage Guide

Learn how to use the Complex Number Division Calculator calculator and its working principles

How to Use the Calculator

Enter the real and imaginary parts of the first complex number (a + bi) in the respective fields.
Enter the real and imaginary parts of the second complex number (c + di) in the respective fields.
Click the "Calculate" button to perform the division.
The result will be displayed in both rectangular form (a + bi) and polar form (r ∠ θ).

Working Principle

The division of two complex numbers (a + bi) / (c + di) is calculated by multiplying the numerator and denominator by the conjugate of the denominator. The formula is:

(ac + bd) + (bc - ad)i / (c² + d²)

This results in a new complex number in rectangular form, which can also be represented in polar form as r ∠ θ, where r is the magnitude and θ is the angle.