In math, imaginary unit, or , is a number that can be represented by equations, but refers to a value that can only exist outside of real numbers. The mathematical definition of the imaginary unit is (i.e., the principal root of ), where satisfies the property .
The reason why was created was to answer a polynomial equation, , which normally has no solution (as the value of would have to equal ). Though the problem is solvable, the square root of could hardly be represented by a physical quantity of objects in real life.
Square root of iEdit
It is sometimes assumed that one must create another number to show the square roots of , but that is not needed. The square roots of can be written as: , a result which can be shown as follows:
Powers of iEdit
The powers of follow a predictable pattern:
This can be shown with the following pattern (where is any integer):