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Re: Teaching by the unqualified thread



When I was in junior high I learned algebra on my own from a very old
"college algebra" textbook. Imaginary and complex numbers intrigued me.
The book said that simple operations (like taking the square root) on real
numbers took you into the realm of complex numbers, but that the operations
on the complex numbers did not require anything more complex. I verified
that many operations on complex numbers led to other complex numbers. But
I tried to think about the most complicated procedure I could come up with,
and it was a complex number raised to a complex power. So I played around
with i^i and, to my surprise, "proved" that it was a real number!
e^(-pi/2). (I didn't realize then that it was multi-valued.) My math
teacher looked at my proof and admitted it was interesting, but felt pretty
sure it was already known - so he was not unqualified.

Having made this discovery thrilled me at the time. Do any of you have
similar stories?

Laurent Hodges