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Sergey15-Moonstone
15-Moonstone
Oct 30, 2023 7:37 PM UTC
Solved

Symbolic operations with complex functions: conjugate, Re and Im

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

 

 

 

Werner_E
Werner_EAnswer
25-Diamond I
Oct 31, 2023 12:41 AM UTC

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

 

 

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13 replies

ttokoro
ttokoro21-Topaz I
21-Topaz I
Oct 30, 2023 11:23 PM UTC

image.pngimage.png

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t.t.
    Werner_E
    Werner_E25-Diamond IAnswer
    25-Diamond I
    Oct 31, 2023 12:41 AM UTC

    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

     

     

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      Werner_E
      Werner_E25-Diamond I
      25-Diamond I
      Oct 31, 2023 12:51 AM UTC

      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.

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        terryhendicott
        terryhendicott21-Topaz II
        21-Topaz II
        Oct 31, 2023 1:23 AM UTC

        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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