Skip to main content
lvl10720-Turquoise
20-Turquoise
Jun 17, 2014 11:00 AM UTC
Solved

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

Hello, Everyone.

min_max_of_f(x).PNG

Thanks in advance for your time and help.

Best Regards.

Werner_E
Werner_EAnswer
25-Diamond I
Jun 17, 2014 11:14 AM UTC

e^2

View in thread

3 replies

Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
Jun 17, 2014 11:14 AM UTC

e^2

Translate
lvl10720-TurquoiseAuthor
20-Turquoise
Jun 17, 2014 12:19 PM UTC

since :

%281%29.PNG

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

Regards.

Translate
Werner_E
Werner_E25-Diamond I
25-Diamond I
Jun 17, 2014 12:34 PM UTC

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

Translate
Terms & ConditionsAccessibility statement