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Re: problem to define a complex quantity

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  • Subject: [mg116893] Re: problem to define a complex quantity
  • From: Daniel Lichtblau <danl at>
  • Date: Thu, 3 Mar 2011 06:00:19 -0500 (EST)

tarun dutta wrote:
> i want to use complex variable such as
> c[i_]=a[i]+I*b[i]    ;where 'a' and 'b' are  both real
> then I get
> conj[c[i]] =a[i]-I*b[i]
> by stating
> conj[x_]:=complexexpand[conjugate[x]];
> but now i am writing
> c[i_][t_]=a[i][t]+I*b[i][t]
> but i am not getting
> conj[c[i][t]]=a[i][t]-I*b[i][t]
> by stating
> conj[x_]:=ComplexExpand[Conjugate[x]]
> moreover am using mathematica version-7
> is there any way of writing this thing?
> give some valuable insight.
> regards,
> tarun

Above, werbatim, is the message I received around a week ago--less the 
part about using version 7, which I needed to guess. Below, verbatim, is 
what I sent in private email response at that time. It turns out that 
the same approach will still work today (I tested it).


The result below looks about right to me.

In[327]:= c[i_][t_] := re[i][t] + I*im[i][t]
conj[a_] := ComplexExpand[Conjugate[a]]

In[329]:= conj[c[i][t]]
Out[329]= -I im[i][t] + re[i][t]

This was in version 8. A bug in earlier versions caused the various 
entities to be regarded as "complex valued". So you would see something 
like below. By the way, it would save people like myself a lot of time 
if you actually show your input and output, so nobody has to guess at 
the nature of teh problem.

Out[4]= -Im[im[i][t]] + I (-Im[re[i][t]] - Re[im[i][t]]) + Re[re[i][t]]

To work around this I'd suggest postprocessing with Simplify, giving 
assumptions that re[i][t] and im[i][t] are both real valued.

Daniel Lichtblau
Wolfram Research

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