Famous Theorems of Mathematics/Euler's equation

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Euler's equation states that,

From which, the famous identity,

may be deduced.

Proof[edit]

Definition 1
Definition 2
Definition 3

The following results will be assumed;

Theorem 1
Proof

By definition 1,

Observe that one may split the summation into two,

Evaluating,

By definition 2 and 3,

Theorem 2
Proof

By theorem 1,

Hence,