In math, imaginary units, or , are numbers that can be represented by equations but refer to values that could not physically exist in real life. The mathematical definition of an imaginary unit is , which has the property .
The reason was created was to answer a polynomial equation, , which normally has no solution as the value of x^2 would have to equal -1. Though the problem is solvable, the square root of -1 could not be represented by a physical quantity of any objects in real life.
Square root of i [change]
It is sometimes assumed that one must create another number to show the square root of , but that is not needed. The square root of can be written as: .
This can be shown as:
Powers of i [change]
The powers of follow a predictable pattern:
This can be shown with the following pattern where n is any integer: