De Moivre's formula

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In mathematics, de Moivre's formula, named after Abraham de Moivre, states that for any complex number z and integer n,

where is the modulus of z, and is the argument of z. Here, is Euler's number, with often being called the polar form of a complex number.

The formula is very important because it connects complex numbers and trigonometry. It can be easily proved using the trigonometry form of complex numbers, induction, and some trigonometrical identities. Furthermore, using this formula any equation of , where w is complex, can be solved.