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Termwise Differentiation

  1. Nov 30, 2011 #1
    Ʃ(2+3i)^(2+i)n

    Since there is no declared z (complex analysis)
    in this problem would we take this differentiation with respect to n?

    If so, my answer was

    Ʃ n(2+3i)^(2+i)n-1
     
  2. jcsd
  3. Dec 1, 2011 #2

    Mute

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    Your description of the problem is too ambiguous. What is your summation variable? Is it i or n? Or is i the imaginary number? And is n supposed to be in the power with (2+i)? Is n supposed to be an integer or can it be any number (real or complex)?
     
  4. Dec 1, 2011 #3
    The summation index is n so 0 to inf and i is an imaginary number. In all the problems we have seen we are given z because z = x + iy, but here none is given..so I'm unsure if it should just be zero or if we should assume this is z^u or u^z? I'm not sure, the professor didn't specify.
     
  5. Dec 1, 2011 #4
    [itex]= \Sigma r^{n}[/itex], with r = (2+3i)^(2+i), but |r| = 4.86... > 1 [itex]\Rightarrow[/itex] the sum diverges, so it doesnt even make sense to define it as a function (at least not in the traditional simple way). Therefore you can't take any derivative.
     
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