Hello, Everyone. Thanks in advance for your time and help. Best Regards.

L

lvl107

20-Turquoise

Solved

( 1 - x1i / 1 + x1i ) and ( ( 1 - x1i / 1 + x1i )^-1i )^1i are equivalent or not ?

Forum|Forum|12 years ago
June 7, 2014
9 replies
3241 views

Hello, Everyone.

Equivalent or not .PNG

Thanks in advance for your time and help.

Best Regards.

1_Equivalent-or-not-xmcd.zip

Other

Best answer by LucMeekes

Maybe depends on which mathematician you ask...

Mathcad 11.2a, with the good old Maple machine, sees them as identical, given the right settings:

Note that the complex expansion of the second term alone is several pages wide.

Success!
Luc

Werner_E

25-Diamond I

The first expression is just one of an infinite number of results of the second one.

P

PhilipOakley

1-Visitor

Try thinking of it as (a^b)^c) and see where the power product gets you.

Werner_E

25-Diamond I

Philip Oakley wrote:
Try thinking of it as (a^b)^c) and see where the power product gets you.

(a^b)^c = a^(b*c) is true and unique for reaI numbers only! I think LoiLe is exactly doing that and is wondering, why Mathcad does not simplify the right expression to the left one.

A number to the power of a complex is not unique as I wrote above but there rather are an infinite number of results. I already elaborated on this a couple of times at replies to other posts of LoiLe but he seems not to be willing to acccept that fact.

I am also wondering, but for different reasons:

It looks on first sight that MC is considering the ambiguity of the expession and is therefor not simplifying the expression on the right by simply multiplying the powers to 1.

But then MC should yield "all" infinite results at least when formulating the expression as an equation and using modifier "fully", but it doesn't as shown in the first example below..

Also 1^i is not unique but MC simplifies it to 1 this time!?? (second example below).