Flipper:

You are trying wayyyyyyyyy to hard.

pi exists because we _can_ draw a circle. That there is no other part
of a circle that relates directly to the diameter or the area, yet we
can still continue to draw them and manipulate and calculate them (even
if a little bit fuzzy around the edges) is enough.

i exists because we _can_ calculate negative areas using square roots.
i takes care of those pesky signs. Keep in mind that something as
obvious as 0 did not exist as a written symbol until relatively
recently, historically.

And so forth. Obvious practical applications of real and imaginary
numbers happen every minute of every day. It hardly matters whether
they 'exist' or not. Their driving concepts do and have existed
forever.

I would refer you to Clarke's Laws here. Many real things exist because
someone somewhere had an idea that flew in the face of received wisdom.
So, as a codicil to "Question Authority", we should establish that
"Received Wisdom Isn't".

http://www.lsi.usp.br/~rbianchi/clarke/ACC.Laws.html

Peter Wieck
Wyncote, PA