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Division of complex power series

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Find tan(z) up to the z^7 term, where tan(z) = sin(z)/cos(z)


    2. Relevant equations
    sin(z) = z - z^3/3! + z^5/5! - z^7/7! + ...

    cos(z) = 1 - z^2/2! + z^4/4! - z^6/6! + ...


    3. The attempt at a solution
    Hi,
    Seeing as sin and cos have the same power series as for when they are real, can you just divide the complex polynomials?

    i.e. (z - z^3/3! + z^5/5! - z^7/7! + ...) / (1 - z^2/2! + z^4/4! - z^6/6! + ...) = z + z^3/3 + 2z^5/15 + 17z^7/315 + ...

    which is tan(z)? (Assuming it has the same complex power series as real power series, considering sin and cos do?)

    Thanks for any help
     
  2. jcsd
  3. Nov 17, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, you can do it that way.
     
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