De Moivre's formula

The Moivresche set, also set of de Moivre formula or by de Moivre called, states that for any complex number (and hence every real number ) x and any natural number n the context

Applies.

He bears his name in honor of Abraham de Moivre, who found that sentence in the first decade of the 18th century.

The formula combines the complex numbers with trigonometry, so the complex numbers can be represented using trigonometry. The expression can also be reduced as shown.

Derivation

The set can Moivresche of the Euler formula

The complex exponential function and its functional equation

Be derived.

An alternative proof follows from the product representation ( see addition theorems )

By mathematical induction.

Generalization

If

Then

But a multi-valued function is not

This is true