The imaginary constant

Imaginary and complex numbers are based around a single letter, which effectively acts as an unknown constant. This is .

The value of

is equal to the square root of . This can be written in either of the following forms:

Simplifying imaginary numbers

The second form has some interesting use-cases. Because we know that , we can rewrite any power of as a simple real number, or as just a coefficient of .

Example: Simplify

Example: Simplify

Example: Simplify