Math

Complex Number to Polar Form Calculator

Convert a + bi into polar form r∠θ.

Calculated Output

Magnitude r 1.414

Angle θ (°) 45

Formula: r = √(a² + b²), θ = atan2(b, a)

Step-by-Step Breakdown

1. Values used:

2. Real part a = 1

3. Imaginary part b = 1 i

5. Magnitude r = 1.414

6. Angle θ = 45°

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The math behind it

r = √(a² + b²) is the modulus and θ = atan2(b, a) is the argument, so a + bi = r(cos θ + i sin θ).

1 + i → r = √2 ≈ 1.414, θ = 45°.

Why use polar form?

It makes multiplication, division and powers of complex numbers much simpler.