Complex Number Polar Form Calculator

Convert complex numbers between rectangular (a + bi) and polar (r∠θ) forms.

Input Mode

Real Part (a)

Imaginary Part (b)

Complex Number

Rectangular Form:

3.0000 + 4.0000i

Polar Form:

5.0000 ∠ 53.13°

Alternative Forms

Euler:

5.0000e^(i·0.9273)

Cis:

5.0000(cos(53.13°) + i·sin(53.13°))

Conjugate (z*)

3.0000 - 4.0000i

|z|²

25.0000

Square Roots (√z)

Root 1: 2.0000 + 1.0000i

Root 2: -2.0000 - 1.0000i

Rectangular → Polar

r = √(a² + b²)

θ = atan2(b, a)

Polar → Rectangular

a = r·cos(θ)

b = r·sin(θ)

Complex arithmetic

Coordinate conversion