Complex to polar form

Convert a+bi to polar form r∠θ where r = |z| and θ = arg(z).

z =

z = a + bi = r(cos θ + i sin θ) = r∠θ, where r = √(a²+b²) and θ = arctan(b/a).

3+4i: r = 5, θ = arctan(4/3) ≈ 53.13° → 5∠53.13°.

Multiplication: multiply moduli, add angles. Division: divide moduli, subtract angles. Powers: De Moivre's theorem zⁿ = rⁿ∠(nθ).