Lemma: Euler's Identity

For $x=\pi,$, the value of the complex exponential function $\exp(ix)=-1.$ Therefore, the following result holds:

\[e^{i\pi}+1=0\]

This result is known as Euler's identity. It is remarkable since it unifies $4$ important numbers in only one equation: * the real number zero $0,$ * the real number one $1,$ * the $\pi$ constant, and * the imaginary unit $i.$

Proofs: 1

Corollaries: 1


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983