Why is e^pi i = -1 weird?

B/c we think of exp as e^x -- an exponential function.
This form makes sense for integers w/o problem, rationals with some
work,
and reals by continuity.
However, what does 2^i mean?
(Or e^i?)
It's simply meaningless -- we get e^z by expanding a power series, and
plugging in complex numbers.
[NB: no analytic continuation issues.]

That's why it's -weird- -- our original interpretation doesn't make
sense any more.

Once you understand exp geometrically (say, as a covering space of lie
groups),
then it's really obvious -- and you see that e^(x+y) = e^x * e^y is
the key property
that guarantees that it behaves like 2^x etc. for reals.
[& why does the imaginary axis wrap around the circle?
 look at d(exp) at z=0 -- imaginary derivative better point -up-]