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# Euler's identity

Euler's identity is the equation ${\displaystyle e^{i\pi }=-1}$, where ${\displaystyle e}$ is the natural logarithm base, ${\displaystyle i}$ is the imaginary unit and ${\displaystyle \pi }$ is the ratio of a circle's circumference to its diameter. The identity is sometimes stated as ${\displaystyle e^{i\pi }+1=0}$.