Imaginary unit
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The imaginary unit, or i, is used in mathematics to pull together the real number system and the complex number system. Its definition is 
and has the property 
.
The reason i was created was to answer a polynomial equation, x2 + 1 = 0, which normally has no solution.
[change] Square root of i
It is sometimes assumed that one must create another number to show the square root of i, but that is not needed. The square root of i can be written as: 
.
This can be shown as:
[change] Powers of i
The powers of i follow a predictable pattern:
- i − 3 = i
- i − 2 = − 1
- i − 1 = − i
- i0 = 1
- i1 = i
- i2 = − 1
- i3 = − i
- i4 = 1
- i5 = i
- i6 = − 1
This can be shown with the following pattern where n is any integer:
- i4n = 1
- i4n + 1 = i
- i4n + 2 = − 1
- i4n + 3 = − i
