### Imaginary unit

The imaginary unit *i* is formally defined as the square root of –1, so

whatever that may be.

##### Explanation

This definition is clearly out of date, but is unfortunately still often used in school books. The current definition of the imaginary unit is

##### Example 1

The ascending powers of *i* give

Because *i*^{4} = 1 this continues with

and these values repeat themselves again and again.

## HistoryThe Italian mathematician Rafael Bombelli published the book |