Re: problem to define a complex quantity

• To: mathgroup at smc.vnet.net
• Subject: [mg116893] Re: problem to define a complex quantity
• From: Daniel Lichtblau <danl at wolfram.com>
• 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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