De Moivre's formula

In mathematics, de Moivre's formula or de Moivre's theorem is an equation named after Abraham de Moivre. It states that for any real number "x" and integer "n", 
formula_1 
The formulation of De Moivre's formula for any complex numbers formula_2 (with modulus formula_3 and angle formula_4) is as follows:
formula_5
Here, formula_6 is Euler's number, and formula_7 is often called the polar form of the complex number formula_2.
The formula is very important because it connects complex numbers and trigonometry. It can be proved using the trigonometry form of complex numbers by mathematical induction, with the help of some trigonometrical identities. It can also be proved using Euler's formula as well. 
By using this formula, any equation of the form formula_9, where "w" is complex, can be solved.