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Large powers of complex numbers 
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#1
Jan2113, 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 


#2
Jan2213, 06:57 AM

Thanks
P: 5,801

What do you think?



#3
Jan2213, 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.



#4
Jan2213, 07:10 AM

Thanks
P: 5,801

Large powers of complex numbers
The problem is about where the error is greater, assuming either method is done numerically.



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