Complex Number Polar Form Calculator

About this calculator

A complex number written as a + bi (rectangular form) can equivalently be expressed in polar form as a modulus r and an argument θ: the modulus r = √(a² + b²) is the number's distance from the origin on the complex plane, and the argument θ = atan2(b, a) is the angle that distance makes with the positive real axis. Polar form makes multiplication, division, and especially exponentiation of complex numbers far simpler than working directly with rectangular coordinates, since moduli multiply and arguments simply add.

This calculator takes the real and imaginary parts of a + bi and returns its modulus and argument. Electrical engineers working with AC circuit phasors, students studying complex analysis, and signal-processing engineers dealing with the frequency domain — where magnitude and phase are the natural way to describe a signal — use it to move between the two standard representations of a complex number.