Complex Number Calculator

Enter two complex numbers in a+bi form. Results are shown in rectangular, polar (r∠θ), and exponential (r·eⁱᵗ) form.

z₁

Operation

z₂

angle in degrees

Rectangular —

Polar —

Exponential —

Frequently Asked Questions

What is a complex number?

A complex number combines a real part and an imaginary part as a + bi, where i is the imaginary unit with i² = −1. The real part a and the imaginary part b are each ordinary real numbers, and together they locate the point (a, b) on the Argand plane. For 2 + 3i the real part is 2 and the imaginary part is 3.

How do I multiply complex numbers?

Multiply two complex numbers by expanding (a + bi)(c + di) with distribution, then use i² = −1 to collect the real and imaginary parts: the result is (ac − bd) + (ad + bc)i. In polar form the moduli multiply and the arguments add instead. For (2 + 3i)(1 − 4i) the result is 14 − 5i.

What is the polar form of a complex number?

Polar form writes a complex number as r∠θ, where r is the modulus — the distance from the origin — and θ is the argument, the angle from the positive real axis. It is equivalent to the exponential form r·eⁱᵗ by Euler’s formula. Polar and exponential forms make multiplication, powers and roots simpler than the rectangular a + bi form.

Is my data sent anywhere?

Your figures stay on your device when you use the complex number calculator. The complex number calculator works in the browser using JavaScript, with no server round-trip at any point, so your numbers are never transmitted. Nothing is logged, stored or shared with a third party. That also means the tool keeps working offline.

Complex Number Calculator

Frequently Asked Questions

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