1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Large powers of complex numbers
Loading...