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How to take derivative of complex number?

  1. Sep 1, 2009 #1
    1. The problem statement, all variables and given/known data
    On the first day of Electromagnetism class, the professor gave this problem to us to solve. I never learn about taking derivative of complex number. Can someone give me some hints?
    his problem was:
    Given P= 0.5 Re(I*V)
    I= V/(A+B)
    A= R+jX , B=Y+ jZ

    V is constant, find the derivative of P with respect to X (dP/dx)



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 1, 2009 #2

    rock.freak667

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    You could simplify VI in terms of the complex variables, then take out the real part (which might just be a function in X only).

    So that P=0.5 Re(I*V)= 0.5f(X)
     
  4. Sep 1, 2009 #3
    thank you for your response, could you be more specific? which part is the real part and which is the imaginery part?
     
  5. Sep 1, 2009 #4

    rock.freak667

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    j or i is used to denote the complex variable √-1, so in A= R+jX, R is the real part (the one without a 'j')
     
  6. Sep 1, 2009 #5
    this is what I did after your hint. VI becomes V^2/A+B, and V^2 is constant so I take it outside, leaving just 1/A+B for differentiation.
    1/A+B = 1/R+jX+Y+jZ. now I am stuck. I dont know how to find dP/dX.
     
  7. Sep 1, 2009 #6

    rock.freak667

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    so 1/(A+B)= 1/(R+jX+Y+jZ)=1/[(R+Y)+(X+Z)j]

    now multiply both the numerator and denominator by the conjugate of (R+Y)+(X+Z)j
     
  8. Sep 1, 2009 #7
    thanks for your hint again, now I got [(R+Y)-j(X+Z)]/[(R+Y)^2+(X+Z)^2]
     
    Last edited: Sep 1, 2009
  9. Sep 1, 2009 #8

    rock.freak667

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    so put that into the form a+jb and then the real part is simply your 'a'
     
  10. Sep 1, 2009 #9
    so the real part is (R+Y)/[(R+Y)^2+(X+Z)^2]. can I take the derivative with respect with X? can I treat R,Y,Z as constant?
     
  11. Sep 2, 2009 #10

    rock.freak667

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    I am not sure what R,Y and Z are supposed to be, but I assume you would.
     
  12. Sep 2, 2009 #11
    thank you again, after I worked it out, I got dP/dX = -0.5(V^2)[2(x+Z)]/(R+Y)[(R+Y)^2+(X+Z)^2]^2
     
  13. Sep 2, 2009 #12
    hi,

    how to find the derivative of [1/(z*sin(z)*cos(z)] from first principles?
    complicated. any recommendations?
     
  14. Sep 2, 2009 #13

    rock.freak667

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    Don't hijack this thread. Start a new one using the definition of the derivative.

    [tex]f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]
     
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