# Root Routes

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Historically, the search for the *square root of minus one,**,* gave rise to the complex numbers. Typically we refer to as . Perhaps the next obvious question is: what is ? Do we need to invent another number, or can be found in the complex plane?

Contributed by: John Kiehl (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: The blue point at is the square root of the red point at -1.

Snapshot 2: Here is the second square root of -1.

It is remarkable that only is needed to allow you to take any root of any complex number to get a complex number. Even more: over the complexes, every polynomial equation has a solution.

## Permanent Citation