large powers of complex numbers

bjnartowt

1. The problem statement, all variables and given/known data

Suppose you raise a complex number to a very large power, z^n, where z = a + ib, and n ~ 50, 500, one million, etc. On raising to such a large power, the argument will shift by n*ArcTan[b/a] mod 2*Pi, and this is easy to see analytically. However, is there less numerical error when z remains in rectangular form, or less when it is converted to rectangular form?


2. Relevant equations



3. The attempt at a solution

voko

What do you think?

bjnartowt

Honestly, I think I'll have to compute Z analytically, and not leave it to a machine to do it.

voko

The problem is about where the error is greater, assuming either method is done numerically.