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

[lvl107]

Hello, Everyone.

Thanks in advance for your time and help.

Best Regards.

[Werner_E · Accepted solution]

e^2

[lvl107]

since :

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

Regards.

[Werner_E]

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:

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!):