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ℂ Complex Number Calculator

Add, subtract, multiply, divide, and raise complex numbers to integer powers. View modulus, argument, and polar form r∠θ for fast complex arithmetic checks.

Complex Number Calculator

Work with complex numbers in a + bi and polar form. Add, subtract, multiply, divide, convert between forms, and raise complex numbers to integer powers.

Inputs

Complex number A

Complex number B

Power of A (integer)

Use De Moivre's theorem to explore powers like A², A³, or A⁻¹.

Results

3 + 2i

1 − 4i

A + B

4 − 2i

A − B

2 + 6i

A × B

11 − 10i

A ÷ B

-0.294118 + 0.823529i

A in polar form

r = 3.605551, θ = 0.588003 rad

B in polar form

r = 4.123106, θ = -1.325818 rad

Aⁿ

5 + 12i (n = 2)

Great for complex arithmetic practiceVisualize modulus and argument immediately

How to use this tool

Enter the real and imaginary parts for complex numbers A and B in a + bi form.
Read off complex addition, subtraction, multiplication, division, and polar form in the results card.
Optionally set an integer n to explore Aⁿ via De Moivre's theorem in this complex number calculator.

Perfect online complex number calculator for courses

Experiment with sums, products, and quotients of a + bi numbers to build intuition.
See modulus and argument to connect algebraic complex arithmetic with the geometric view in the complex plane.
Use powers of A to explore rotations and scaling using r∠θ and cis(θ) forms.

What this complex number calculator supports

Addition, subtraction, multiplication, and division of complex numbers in a + bi form.
Conversion between rectangular form a + bi and polar / cis form (r, θ).
Integer powers of a complex number using De Moivre's theorem in polar form.

FAQ

Are angles in degrees or radians in this complex calculator?: Angles are reported in radians, which is standard in most maths and engineering courses. Convert to degrees by multiplying by 180/π if needed.
Can I compute square roots or roots of complex numbers?: You can approximate them using powers with fractional exponents, but this tool focuses on integer powers. Many common exam questions can be written using integer powers and basic arithmetic.
What happens if B is 0 when dividing complex numbers?: Division by zero is undefined for complex numbers just like real numbers, so the calculator shows a clear warning for A ÷ B.

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