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MATHEMATICS Complex Analysis Euler's Identity

Euler's Identity

Euler's Identity connects five fundamental constants in a stunningly simple equation

31 Oct 2025

Why does Euler's Identity e^(iπ) equal -1 according to Euler's formula?

Because cos(π) = -1 and sin(π) = 0, so e^(iπ) = cos(π) + i sin(π) = -1. Because i squared equals 1, making e^(iπ) simplify to -1. Because π and i cancel each other out, leaving e raised to zero.