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.
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