Imaginary Unit - Simple English Wikipedia

# Imaginary Unit

### From Wikipedia, a free encyclopedia written in simple English for easy reading.

The Imaginary Unit, or i, used in mathematics to pull together the real number system and the complex number system. Its definition depends on how it is used.

The reason i was created was to answer a polynomial equation, f(x) = 0, which normally has no solution. Also, the equation x2 + 1 = 0 has no solution. Specifically, .

## [edit] 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:

## [edit] 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

## [edit] See Also

- Complex number
- Real number
- Euler's Identity

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