eiθ = cos θ + i · sin θ

Euler's Formula — the most beautiful equation in mathematics

Angle θ
0.000
cos θ (real)
1.000
sin θ (imag)
0.000
|e^iθ|
1.000
θ = 0.000 rad

The Helix — Euler's Formula in 3D (Re · Im · θ)

What is Euler's Formula?

eiθ = cos θ + i · sin θ It says that raising e to an imaginary exponent iθ produces a point that travels around the unit circle in the complex plane. The real part traces a cosine wave; the imaginary part traces a sine wave. At θ = π the point reaches −1, giving the famous identity: eiπ + 1 = 0 Five fundamental constants — e, i, π, 1, 0 — united in a single equation.