Re: Re: More strange behavior by ComplexExpand

*To*: mathgroup at smc.vnet.net*Subject*: [mg60678] Re: [mg60607] Re: [mg60603] More strange behavior by ComplexExpand*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 24 Sep 2005 02:55:23 -0400 (EDT)*References*: <200509210720.DAA08138@smc.vnet.net> <200509220608.CAA01807@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 22 Sep 2005, at 15:08, Andrzej Kozlowski wrote: > This expression is completely correct. ComplexExpand is allowed to > return imaginary numbers in its output, even if the input is real. It has occured to me that this may not be so obvious so perhaps it might be a good idea to illustrate it. In Raul's case the expression to which ComplexExpand was applied was not actually "real": it was only real when the parameter a was assumed to be positive. But ComplexExpand may produce a seemingly complex expression even when applied to something that is unambiguously real, in fact even a numeric real. Here is an example: ComplexExpand[1 - ArcTan[Sqrt[5]], TargetFunctions -> {Abs}] 1 - (1/2)*I*Log[1 - I*Sqrt[5]] + (1/2)*I*Log[1 + I*Sqrt[5]] even though ComplexExpand[Im[1 - ArcTan[Sqrt[5]]]] 0 I don't think this can happen with the default setting of TargetFunctions ->{Re,Im} but still this illustrates can return seemingly non-real forms even for purely real input (not just real parameters). (Of course I think this is just as it should be). Andrzej Kozlowski

**References**:**More strange behavior by ComplexExpand***From:*Raul Martinez <raulm231@comcast.net>

**Re: More strange behavior by ComplexExpand***From:*Andrzej Kozlowski <andrzej@yhc.att.ne.jp>