ℂ Complex Number Calculator

About the Complex Number Calculator

This calculator runs entirely in your browser. It performs the most common complex number operations: addition, subtraction, multiplication, division, modulus (absolute value), conjugate, and argument (angle). Enter the real and imaginary parts of A and B, pick an operation, and the result appears instantly.

Complex number formulas

• Addition — (a+bi) + (c+di) = (a+c) + (b+d)i.
• Subtraction — (a+bi) − (c+di) = (a−c) + (b−d)i.
• Multiplication — (a+bi)(c+di) = (ac−bd) + (ad+bc)i.
• Division — (a+bi)/(c+di) = [(ac+bd) + (bc−ad)i] / (c²+d²). Requires B ≠ 0 (both c and d not zero).
• Modulus — |a+bi| = √(a² + b²). The distance from the origin in the complex plane.
• Conjugate — conj(a+bi) = a − bi. Reflects across the real axis.
• Argument — arg(a+bi) = atan2(b, a) in degrees. The angle from the positive real axis; undefined when A = 0.

How to use the calculator

1. Enter the real and imaginary parts of complex numbers A and B.
2. Click the button for the operation you need.
3. The result appears below. Each button can be pressed repeatedly.

Frequently asked questions

What happens if I divide by zero? Division by a complex number B = 0 (both real and imaginary parts zero) is undefined. The calculator shows an error message in that case.

What units is the argument in? Degrees, rounded to 4 decimal places, in the range −180° to 180°.

Can I use negative imaginary parts? Yes. Enter a negative number for the imaginary part — the calculator handles all sign combinations correctly.

Is my input stored or uploaded? No. Everything happens in your browser. Your input is never sent to a server.