Complex Number Calculator

Perform operations with complex numbers. Free online complex number calculator.

The Complex Number Calculator performs arithmetic and operations with complex numbers in the form a + bi. Add, subtract, multiply, divide, find conjugates, magnitudes, and convert between rectangular and polar forms. Essential for electrical engineering, signal processing, quantum mechanics, and advanced mathematics.

Common use cases

  • Electrical circuit analysis (impedance)
  • Signal processing (Fourier transforms)
  • Quantum mechanics
  • Control systems
  • Advanced mathematics

How to use

  1. Enter complex numbers (a+bi format)
  2. Select the operation
  3. Click calculate for results
  4. View rectangular and polar forms
  5. See step-by-step solution

FAQ

What is i?

i is the imaginary unit, defined as √(-1). i² = -1.

How do I multiply complex numbers?

(a+bi)(c+di) = (ac-bd) + (ad+bc)i. Use FOIL and remember i² = -1.

What is the conjugate?

The conjugate of a+bi is a-bi. Useful for division: multiply by conjugate.

What is polar form?

r(cos θ + i sin θ) or re^(iθ), where r = magnitude, θ = angle. Useful for multiplication/powers.