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:
x2 + 9 = 0
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
i22 = (i4)5 · i2 = − 1
i27 = −i
