Imaginary unit

square root of negative one, used to define extra-dimensional complex numbers

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 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 iEdit

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 iEdit

The powers of   follow a predictable pattern:

 
 
 
 
 
 
 
 
 
 

This can be shown with the following pattern where n is any integer:

 
 
 
 

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