Imaginary Numbers

Imaginary Unit

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

Imaginary Unit

Imaginary Numbers

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:

x2 + 9 = 0

Imaginary Numbers

Powers of the Imaginary Unit

i0 = 1

i1 = i

i2 = −1

i3 = −i

i4 = 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.

i22

Imaginary Number Operations

i22 = (i4)5 · i2 = − 1

i27 = −i