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Derivative of an imaginary number

  1. Jan 20, 2004 #1
    I was just wondering if anyone knows the rule when taking the derivative of an imaginary number(i). For example: d(ix)/dx=?

    Thanks:)
     
  2. jcsd
  3. Jan 20, 2004 #2

    mathman

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    For the purposes of differential calculus, i is simply another constant.
    Therefore d(ix)/dx=idx/dx=i
     
  4. Jan 23, 2004 #3

    HallsofIvy

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    You don't take the derivative of "numbers" in general. You take the derivative of functions. Of course you can treat any number, including complex numbers, as a "constant function". As "mathman" said (and he ought to know!) d(ix)/dx= i just as d(ax)/dx= a for any number a.

    If you allow the variable, x, to be a complex number, then it becomes more interesting!
     
  5. Sep 2, 2009 #4
    how can i proof if this function has a derivative?

    1/[ z*sin(z)*g(z)] from first principle?

    z= x + jy.
     
  6. Sep 2, 2009 #5

    HallsofIvy

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    You don't- not with information on g. And, whatever g is, that function is certainly NOT differentiable where it is not defined: any multiple of [itex]\pi[/itex].
     
  7. Sep 2, 2009 #6
    suppose to be

    1/[ z*sin(z)*cos (z)]
     
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