What operations does this support?

Typically addition, subtraction, multiplication, and division of complex numbers in the form a + bi, where i is the imaginary unit (√-1).

How is complex number multiplication calculated?

(a + bi)(c + di) = (ac − bd) + (ad + bc)i, using the distributive property and the fact that i² = −1.

Where are complex numbers used practically?

They're essential in electrical engineering (AC circuit analysis), signal processing, and quantum mechanics, among other fields.

Complex Number Calculator | CalculatorLabs.net

Complex Number Calculator

Add, subtract, multiply, or divide two complex numbers, and find the resulting modulus and argument.

Real Part (a) of z₁

Imaginary Part (b) of z₁

Real Part (c) of z₂

Imaginary Part (d) of z₂

Operation

What Is the Complex Number Calculator?

This calculator adds, subtracts, multiplies, or divides two complex numbers in the form a + bi, and also reports the resulting modulus and argument.

Formula

Multiplication: (a+bi)(c+di) = (ac−bd) + (ad+bc)i. Division multiplies both parts by the conjugate of the denominator. Modulus: |z| = √(re² + im²). Argument: θ = atan2(im, re).

How to Use This Calculator

Enter the real and imaginary parts of the first complex number (z₁).
Enter the real and imaginary parts of the second complex number (z₂).
Choose the operation: add, subtract, multiply, or divide.
Click Calculate to see the result, modulus, and argument.

Worked Example

Multiplying z₁ = 3 + 2i by z₂ = 1 + 4i gives (3×1 − 2×4) + (3×4 + 2×1)i = −5 + 14i, with a modulus of about 14.87.

Tips

Division is undefined when the second complex number is 0 + 0i. The argument is measured counter-clockwise from the positive real axis, in degrees.