Proposition: Euler's Formula

According to the definitions of the unit circle in the complex plane and the real functions cosine \(\cos:\mathbb R\mapsto \mathbb R\) and sine \(\sin:\mathbb R\mapsto \mathbb R\) we get the result

\[\exp(ix)=\cos(x)+i\sin(x).\]

This result is known as Euler's formula.

Proofs: 1

Proofs: 1 2 3 4


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References

Bibliography

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