# Imaginary Numbers

### Imaginary Unit

The** imaginary unit ** is the number and is designated by the letter *i.*

### Imaginary numbers

An** imaginary number** is denoted by** bi**, where:

**b** is a real number.

** i** is the imaginary unit.

With imaginary numbers, roots with an index pair and negative roots can be calculated:

x^{2} + 9 = 0

## Powers of the Imaginary Unit

**i**^{0} = 1

**i**^{1} = *i*

**i**^{2} = −1

**i**^{3 } = −*i*

**i**^{4} = 1

The values are repeated in groups of four, therefore, to know the value of a particular power of * i*, divide the exponent by 4, and the remainder is the exponent of the power equivalent to that given.

*i*^{22 }

*i*^{22 } = (*i*^{4})^{5} · *i*^{2} = − 1

*i*^{27 } = −*i*

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