Re: Getting Symbolic Real and Imag Parts? (Once Again)

• To: mathgroup at smc.vnet.net
• Subject: [mg33508] Re: Getting Symbolic Real and Imag Parts? (Once Again)
• From: aes <siegman at stanford.edu>
• Date: Sun, 24 Mar 2002 01:44:03 -0500 (EST)
• Organization: Stanford University
• References: <a7cs6t\$hv8\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thanks to several people who emailed me to point out that the way to get
symbolic real and imag parts of an expression is

Real part =  ComplexExpand[Re[expr]]

Imag part =  ComplexExpand[Im[expr]]

and also my apologies for belatedly realizing that I had raised this question
once before, months ago; gotten the same answer; and forgotten it.  It's now
stored in my online collection on Mathematica hints and kinks.

Might as well also repeat the same comment that I made last time, however,
namely that writing the expression in this form seems syntactically bizarre, not
so say nonsensical.  The expression

ComplexExpand[Re[Sin[a + I b]]]

would normally be interpreted as saying, in words, "Do a complex expansion of
the real part of the sine of a + I B", presumably producing a complex result,
including adding a "+ I 0" to make the result complex.

What's really wanted, however, and what's actually accomplished by this
expression, is instead, "Take the real part of the complex expansion of the sine
of a + I b", a result you would expect to be written as

Re[ComplexExpand[Sin[a+I b]]]

It's sort of like having to write  Log[Sin[z]]  when what you want is
Sin[Log[z]]

> OK,  so you can use ComplexExpand expand to find the symbolic real and imag
> parts of an expression -- e.g. the input
>
>       zComplex = ComplexExpand[ Sin[a+I b], TargetFunctions->{Re,Im}]
>
> gives as output
>
>       Cosh[b] Sin[a] + I Cos[a] Sinh[b]
>
> as desired.  But now, how do I get Mathematica to peel out the symbolically
> real and
> imaginary parts of this? -- that is, what inputs
>
>       zR = ???
>
>       zI = ???
>
> will give as outputs
>
>       Cosh[b] Sin[a]
>
> and
>
>       Cos[a] Sinh[b]
>
> (Maybe an example in the ComplexExpand Help file would be helpful?)

```

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