Complex Number Explorer

Complex Numbers Input

z₁ = a + bi

Real (a):1.0

Imaginary (b):2.0

1 + 2i

z₂ = c + di

Real (c):3.0

Imaginary (d):-1.0

3 − 1i

Operation:

Properties

|z₁| modulus: —

arg(z₁) degrees: —

|z₂| modulus: —

arg(z₂) degrees: —

Polar form z₁ = r·e^(iθ):

—

Polar form z₂ = r·e^(iθ):

—

Result:

—

De Moivre (z₁ⁿ form):

—

Presets

                    Formula Reference:

                    z = a + bi = r·e^(iθ)

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

                    z·z̄ = |z|² = a² + b²

                    De Moivre: zⁿ = rⁿ·(cos nθ + i·sin nθ)