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Re: question: How to get Mathematica to show more than one value of a complex valued function?

• To: mathgroup at smc.vnet.net
• Subject: [mg46328] Re: [mg46286] question: How to get Mathematica to show more than one value of a complex valued function?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 14 Feb 2004 04:38:05 -0500 (EST)
• References: <200402140256.VAA08476@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 14 Feb 2004, at 03:56, steve_H wrote:

> hello;
>
> this is Mathematica 5.0
>
> given a multi-valued complex function, how can I get Mathematica to 
> show
> more than one value? or to show the general formula for all solutions?
>
> for example, (-i)^i  is multivalued. The result returned by 
> Mathematica is
> Exp[Pi/2], which is the first possible value. But there are infinitly 
> many
> others (if my math is correct), such as Exp[-3/2 Pi], Exp[5/2 Pi] 
> etc...
> where the general function value is Exp[Pi/2 +-  2 n Pi]  
> n=0,1,2,3,....
>
> Same as for Log[z] where z is a complex number, which is multi-valued.
>
> or can I at least tell Mathematica to tell me if the result returned 
> is the ONLY
> one possible, (i.e. the complex function is NOT multi-valued)? becuase
> right now it is not clear from the result if result returned is the 
> only
> value or if there are others.
>
> thanks,
> Steve
>
Mathematica returns in such cases the so called principal value. 
However, in version 5  you can get multivalued answer by using:


Reduce[x^I == -I, x]


C[1] $B":(B Integers &&
   x == E^((-I)*(2*I*Pi*C[1] -
       (I*Pi)/2))

etc


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

• References:
  • question: How to get Mathematica to show more than one value of a complex valued function?
    • From: nma124@hotmail.com (steve_H)