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lvl10720-Turquoise
20-Turquoise
June 17, 2014
Solved

min/max of complex function, ( 1i + x / 1i - x )^( 1i / atan(x) ) ?

  • June 17, 2014
  • 3 replies
  • 1507 views

Hello, Everyone.

min_max_of_f(x).PNG

Thanks in advance for your time and help.

Best Regards.

Best answer by Werner_E

e^2

3 replies

Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
June 17, 2014

e^2

L
lvl10720-TurquoiseAuthor
20-Turquoise
June 17, 2014

since :

%281%29.PNG

what value of x then f(x) get min/max ?

Regards.

Werner_E
Werner_E25-Diamond I
25-Diamond I
June 17, 2014

any (if you trust the numerics).

Here is something for you to think about. I have said it many, many times - you may like it or not, but the exponentialisation of a complex has an infinite number of results. So the questions you ask here don't make much sense! Sorry!

Mathcad, like you, is not fully (or not at all) aware of that ambiguity and will give you different results, depending on the situation:

1.png

I doubt that the negative symbolic result for f(1) is valid at all!

"All" results just for f(1) can be obtained by arbitrary chosing two integer values for n and k (and all are positive!):

2.png

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