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Algebraic Manipulation
Posted:
Jan 15, 1999 2:54 PM
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I agree with Jerry Uhl -- why are complex numbers and especially
complex exponentials so poorly taught in high school?
Most texts give DeMoive's theorem, so people learn that
(cis theta)^n = cis (n theta)
but then they fail to make the connection that this means that "theta"
is acting like the exponent of something, and in fact
e^(i theta) = cis theta
and finally to go on from there to do tricks like you discuss (analyze
the behavior of e^-x cos(4x) by using e^((-1 + 4i)x) and so forth).
It's beautiful math, it's useful, it's fun, it's easy ... it should be
teacher's favorite thing about trigonometry class.
My question above wasn't purely rhetorical -- why IS this topic so
little emphasized in the high school curriculum? Or, maybe
equivalently, what topics can we get rid of and replace with this?
--Joshua Zucker
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