The exponential form of a complex number

Let some complex number be written in trigonometric form z = r * (cos φ + isin φ), then in an indicative form it can be represented as . If we equate both obtained numbers and reduce by r, then we obtain an equation, which is called the Euler formula and shows that expressions and have the same logical entity.

Formulas for multiplication, division, exponentiation, and root extraction are written as follows:





, where k = 0, 1, 2, ..., (n - 1).