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Large powers of complex numbers

by bjnartowt
Tags: complex, numbers, powers
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bjnartowt
#1
Jan21-13, 07:55 PM
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
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voko
#2
Jan22-13, 06:57 AM
Thanks
P: 5,795
What do you think?
bjnartowt
#3
Jan22-13, 07:00 AM
P: 273
Honestly, I think I'll have to compute Z analytically, and not leave it to a machine to do it.

voko
#4
Jan22-13, 07:10 AM
Thanks
P: 5,795
Large powers of complex numbers

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


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