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?)