Arithmetic and analysis on complex numbers in rectangular (a + bi) or polar (r·eiθ) form. Computes both forms, modulus, argument, conjugate, powers, nth roots, exp, log, and renders the Argand plane.
A complex number z = a + bi can also be written z = r(cos θ + i sin θ) = r·eiθ with r = |z| = √(a² + b²) and θ = arg(z) = atan2(b, a). Multiplication scales magnitudes and adds angles; division does the opposite. De Moivre's theorem gives zn = rn·einθ. The k k-th roots of z sit on a circle of radius r1/k equally spaced by 2π/k, starting at angle θ/k. The principal logarithm is log z = ln r + iθ with θ in (-π, π].