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lvl10720-Turquoise
20-Turquoise
Jun 30, 2014 6:13 AM UTC
Solved

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

Hello, Everyone.

Equivalent or Not.PNG

Thanks in advance for your time and help.

Best Regards.

LucMeekesAnswer
23-Emerald V
Jun 30, 2014 8:32 PM UTC

I guess not, since there are too many solutions:

atan.png

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

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6 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
Jun 30, 2014 9:21 AM UTC

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.

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lvl10720-TurquoiseAuthor
20-Turquoise
Jun 30, 2014 6:29 PM UTC

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 :

Correct+the+question.PNG

Thanks again.

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Werner_E
Werner_E25-Diamond I
25-Diamond I
Jun 30, 2014 10:41 PM UTC

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

1.png

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lvl10720-TurquoiseAuthor
20-Turquoise
Jun 30, 2014 6:34 PM UTC

And I have the similar question :

The+Second+Solution.PNG

Thanks in advance for your time and help.

Best Regards.

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LucMeekes23-Emerald VAnswer
23-Emerald V
Jun 30, 2014 8:32 PM UTC

I guess not, since there are too many solutions:

atan.png

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

Translate
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