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Root Routes

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show blue's angle
show red's angle
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Historically, the search for the square root of minus one,
-1
, gave rise to the complex numbers. Typically we refer to
-1
as
i
. Perhaps the next obvious question is: what is
i
? Do we need to invent another number, or can
i
be found in the complex plane?
The figure shows the complex number plane. The circle is the unit circle with -1 and
i
labeled. As you drag the blue point, the red point shows you its squared value, that is,
red=
2
blue
. So, of course, putting the blue point on
i
puts the red point on -1. Where do you put the blue point to put the red point on
i
? Can you find a second solution? Don't forget every nonzero number has two square roots!
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