Skip to content
WPCalc Wise People Calculate

Complex Number Calculator

The Complex Number Calculator is a helpful tool for performing operations with complex numbers, such as addition, subtraction, multiplication, and division. It’s ideal for students, engineers, and anyone working with imaginary numbers in mathematics or physics. Just input the real and imaginary parts to instantly get the result of your selected operation.

Complex Number Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Complex Number Operations Formula

Formula
\[ (a + bi) \pm (c + di) = (a \pm c) + (b \pm d)i \] \[(a + bi)(c + di) = (ac – bd) + (ad + bc)i\] \[\frac{a + bi}{c + di} = \frac{(a + bi)(c – di)}{c^2 + d^2} = \frac{ac + bd}{c^2 + d^2} + \frac{bc – ad}{c^2 + d^2}i\]

These formulas allow you to perform addition, subtraction, multiplication, and division with complex numbers, where i is the imaginary unit $$(i^2 = -1)$$.

Complex numbers are used when solving equations that have no real solutions, particularly in fields such as electrical engineering, quantum mechanics, and signal processing. A complex number has the form $$a + bi$$, where $$a$$ is the real part and $$b$$ is the imaginary part. This calculator helps automate the operations so you can focus on solving higher-level problems. Simply enter both numbers and choose the operation — the tool will compute the correct result, showing both the real and imaginary components.

Previous
Complex Number to Polar Form
Next
Modulus of Complex Number

Leave a Reply

Your email address will not be published. Required fields are marked *