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Homework Help: Large powers of complex numbers

  1. Jan 21, 2013 #1
    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. jcsd
  3. Jan 22, 2013 #2
    What do you think?
  4. Jan 22, 2013 #3
    Honestly, I think I'll have to compute Z analytically, and not leave it to a machine to do it.
  5. Jan 22, 2013 #4
    The problem is about where the error is greater, assuming either method is done numerically.
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