What is the Complex Number Calculator?
Calculate complex number operations online with step-by-step work. Add, subtract, multiply, and divide a + bi expressions, find conjugate, modulus, argument, convert between rectangular and polar form, and raise complex numbers to integer powers using De Moivre's theorem. Free, private, and instant in your browser.
How to use the Complex Number Calculator
- Choose an operation (add, multiply, polar conversion, etc.).
- Enter z₁ as real and imaginary parts (or r and θ for polar-to-rectangular).
- Enter z₂ or power n when the operation requires them.
- Read the complex, scalar, or polar result with full steps.
- Copy the formatted result.
Common use cases
- Multiplying (1 + 2i)(3 + 4i) for algebra homework
- Converting 5∠53° to rectangular form
- Finding |3 + 4i| and arg(z) quickly
Frequently asked questions
- What complex operations are supported?
- Add, subtract, multiply, divide, conjugate, modulus, argument, rectangular ↔ polar conversion, and integer powers.
- How is division handled?
- z₁ ÷ z₂ is computed by multiplying the numerator by the conjugate of z₂ and dividing by |z₂|².
- What angle unit is used?
- Polar angles and arguments are shown in degrees (0°–360°).
- Can I compute zⁿ for any n?
- Integer powers use De Moivre's theorem in polar form. Non-integer exponents are not supported.
