Imaginary unit

From Wikipedia, the free encyclopedia

The English used in this article or section may not be easy for everybody to understand. You can help Wikipedia by making this page or section simpler.

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

i^{4n + 1} = i

i^{4n + 2} = − 1

i^{4n + 3} = − i

[change] See Also

• Complex number
• Real number
• Euler's Identity