# large powers of complex numbers

by bjnartowt
Tags: complex, numbers, powers
 P: 273 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
 PF Patron Thanks P: 4,459 What do you think?
 P: 273 Honestly, I think I'll have to compute Z analytically, and not leave it to a machine to do it.
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P: 4,459

## large powers of complex numbers

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

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