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"Real" and "Imaginary" are taken too literally by most students.
I have a tough time convincing them that the imaginary part of the
complex exponential is just as good a solution as the real part. "Real" and
"Imaginary" are just historical terms and don't mean "physical" and
"unphysical". ...
"Indeed, when you discover how powerful complex numbers are for the first
time, it is not unusual for the heavens to open and for choirs of angels to be
heard singing. At least that was my experience. JSM"