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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
  • 3712 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

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

image.pngimage.png

t.t.
    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

     

     

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

      Just an additional note: You don't need to provide a guess value if you evaluate the solve block (find) symbolically.

       

      To the community: Since which version of Prime has it been possible to evaluate solve blocks symbolically again?
      This feature of real Mathcad was broken when Prime entered the stage and I wasn't aware that this option had been reintroduced.
      I just tried with Prime 6 and it does not work but I never had installed P7 and P8, so all I can say that it works in P9.

      Inserting a region with a symbolic evaluation as a line in a program still does not work as it did in Mathcad, though.

        T
        21-Topaz II
        terryhendicott21-Topaz II
        21-Topaz II
        October 31, 2023

        What’s New in PTC Mathcad Prime 9.0.0.0
        In this document, find topics introducing the enhancements in this release. Enhancements are categorized by functional area.
        •Application Enhancements
        ◦Text Styles
        ◦Gradient Operator
        ◦Internal Links
        •Symbolic Engine Enhancements
        ◦Symbolic Solving of ODEs
        ◦Logarithmic Integral Functions
        ◦Elliptic Integral Functions
        ◦Symbolic Solve Block (find)
        ◦Symbolic Assumption on Function
        ◦Definite Integral with complex limits
        ◦Improvement of Calculus Operators
        ◦General keyword improvements
        ◦General function improvements
        •Numeric Engine Enhancements
        ◦PDESolve in Solve Block
        ◦General function enhancements
        •Usability Enhancements
        ◦Custom Color Picker
        ◦Go-to Page
        ◦Current Page Tooltip
        ◦Math region to Text region conversion

        Cheers

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