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)