ATDTDA (7): 201-203 decoding

[Monte Davis]

> Take for  example the diagonal of a 1cm square, mathematically
> it's infinite... 1.414213...

OK, for starters it's not infinite but irrational -- a quantity whose
decimal expression goes on without stopping (another way of saying it can't
be expressed as a ratio of integers, hence "irrational." But that infinite
string of digits, like that of pi, does converge on a *finite* value. As you
say, the square's diagonal does end.

I'm not qualified to go far into complex numbers as math, but from a
mathematical physics PoV you won't go far if you think of them as analogous
to vectors: a quantity with both a scalar magnitude *and* a direction. (The
most familiar example: speed, "50 mph," is a scalar. Velocity, "50 mph going
NNW," is a vector.)

There are formally consistent rules for combining vectors: I'm sailing X
fast thataway, the current is carrying me Y fast thisaway, and I can derive
the resulting course. The rules for operations with complex numbers can be
thought of as a generalization of those, without the restrictions specific
to spatial vectors. That was done originally for the pure-math fun and
beauty of it, but turned outto be just the ticket for calculations with less
familiar vector quantities -- like AC electrical current, which has a
magnitude (amperage) *and* a constantly changing direction (the phase).

(Well, you asked)