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