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Sergey15-Moonstone
15-Moonstone
October 30, 2023
Solved

Symbolic operations with complex functions: conjugate, Re and Im

  • October 30, 2023
  • 2 replies
  • 3711 views

Hello!

 

I am struggling a bit with the symbolic representation of some complex problems. Please, take a look at the attached file. 

How can I properly define complex function on form z=r*e^(i*phi)? Should I write z(r,phi)=r*e^(i*phi)? If I do so, then the symbolic evaluation of complex potentials (Phi and Psi) doesn't get along. Also, I am trying to use Re and Im functions to define the real and Imaginary parts of "z" without any success. The same goes to the conjugate of "z": it should be z*=r*e^(-i*phi).

Hopefully somebody can help me out.

 

UPDATE:

I did some progress, but still can't define properly function "z" without Mathcad telling that some variable is undefined. Updated sheet is attached.

 

Best regards, Sergey

 

 

 

Best answer by Werner_E

Defining z as a function with the arguments r and phi would be the preferred way if you want it actually to be seen as a function, but it works both ways.

z as a function:

Werner_E_0-1698712836983.png

 

z as a variable:

Werner_E_1-1698712889686.png

 

 

2 replies

T
21-Topaz I
ttokoro21-Topaz I
21-Topaz I
October 30, 2023

image.pngimage.png

    W
    Werner_E25-Diamond IAnswer
    25-Diamond I
    October 31, 2023

    Defining z as a function with the arguments r and phi would be the preferred way if you want it actually to be seen as a function, but it works both ways.

    z as a function:

    Werner_E_0-1698712836983.png

     

    z as a variable:

    Werner_E_1-1698712889686.png

     

     

      S
      Sergey15-MoonstoneAuthor
      15-Moonstone
      October 31, 2023

      How would you performed the symbolic derivation of the function z? When z is defined as a function of r and phi, the derivative is zero. 

       

      Sergey_0-1698736893232.png

      Sergey_1-1698736911702.png

       

       

      T
      21-Topaz I
      ttokoro21-Topaz I
      21-Topaz I
      October 31, 2023

      image.pngimage.pngimage.pngimage.png

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