if z := { -1i + [ 2i / ( 1i + x / 1i - x ) + 1 ] } , atan(z) and 1i*atanh(z) are Equivalent or Not in Mathcad ?

[lvl107]

Hello, Everyone.

Thanks in advance for your time and help.

Best Regards.

[Werner_E]

Give us more information! Why do you think those expressions could/would/should be equivalent?

And if you just want to know if Mathcad thinks they are equivalent you will have to ask Mathcad.

[lvl107]

Many thanks, Werner . I guess I have been reminded about my question. I am sorry. I have asked with the incorrect question. And my question would be like the below. And Mathcad has answered completely my question :

Thanks again.

[Werner_E]

You can have all of these, but what for???

[lvl107]

And I have the similar question :

Thanks in advance for your time and help.

Best Regards.

[LucMeekes · Accepted solution]

I guess not, since there are too many solutions:

so z=1 is an exception, and z=-1 is another. I guess those exceptions become obvious if you care to write the atan and the atanh in their exponential forms.

Success!
Luc

[Werner_E]

What are you doing here?

You demand that Mathcad solves an equations which (at least for Mathcad as it isn't aware of all ambiguities) is an identity. So for Mathcad any z is "solution". Why do you think there only are two???

So Mathcad gives the identity

and you can use

but: TO ACHIEVE WHAT?