Euler's formula e^(iθ) = cos θ + i sin θ unites exponentials with rotation in the complex plane. Set θ = π and you get e^(iπ) + 1 = 0.
From beauty to engineering
AC circuit analysis, quantum phase factors, and Fourier transforms all depend on complex exponentials. Euler's identity is not decoration — it is machinery.
Explore interactively
Open equation page