Imaginary unit

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In math, imaginary unit, or , is a number that can be represented by equations, but refers to a value that can only exist outside of real numbers. The mathematical definition of the imaginary unit is (i.e., the principal root of ), where satisfies the property .[1][2]

The reason why was created was to answer a polynomial equation, , which normally has no solution (as the value of would have to equal ). Though the problem is solvable, the square root of could hardly be represented by a physical quantity of objects in real life.

Square root of i[change | change source]

It is sometimes assumed that one must create another number to show the square roots of , but that is not needed. The square roots of can be written as: , a result which can be shown as follows:

Powers of i[change | change source]

The powers of follow a predictable pattern:

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

Related pages[change | change source]

References[change | change source]

  1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-10.
  2. Weisstein, Eric W. "Imaginary Unit". mathworld.wolfram.com. Retrieved 2020-08-10.