Complex Number Polar Form Calculator

About this calculator

Every complex number a + bi can be rewritten in polar form as r(cos θ + i sin θ), where the modulus r = √(a² + b²) is its distance from the origin on the complex plane, and the argument θ = atan2(b, a) is the angle it makes with the positive real axis. This form turns multiplication and division of complex numbers into simple addition/subtraction of angles and multiplication/division of magnitudes — far easier than working directly with the rectangular a + bi components.

Electrical engineers rely on polar form constantly for phasor analysis of AC circuits, where voltage and current are represented as complex numbers with magnitude and phase angle; it's equally central to signal processing (Fourier transforms), control systems, and any physics involving oscillations and rotations.