a+bi ↔ polar · drawn live

🌀 Complex Numbers

Add, subtract, multiply and divide complex numbers, convert to polar form r∠θ, take conjugates, reciprocals and nth roots. Every value is drawn as an arrow on the plane, so you SEE what multiplication does.

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z₁z₂result

nth roots of z₁

Inputs accept a+bi, 3i, -i, plain numbers, decimals — spaces optional. Multiplication in polar: multiply the lengths, ADD the angles (that's why i² rotates to −1). The n roots of a number sit evenly spaced on a circle.