Re: Conjugate of symbolic expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg108084] Re: Conjugate of symbolic expressions
- From: AES <siegman at stanford.edu>
- Date: Mon, 8 Mar 2010 06:11:47 -0500 (EST)
- Organization: Stanford University
- References: <hmvqlg$1gg$1@smc.vnet.net>
In article <hmvqlg$1gg$1 at smc.vnet.net>,
Joseph Gwinn <joegwinn at comcast.net> wrote:
> A typical form would be S1 = Exp[k1*x + I*omega*(t+tau)], describing
> signal one, where K1 is the attenuation in nepers per meter, I is the
> square root of minus one, omega is the angular frequency in radians
> per second, t is time and tau is a fixed time delay, t and tau being
> in seconds.
>
> Often I need the complex conjugate of S1, so I write Conjugate[S1].
You don't know what a firestorm you may ignite with this query.
How would you do this on paper? All the other factors in your
expression you know are going to be purely real, so you really
just want to change I to -I, right? (How else does one take a
CC in the real world?)
And so in Mathematica you might write
S1Complex = S1 /. {I -> -I}
If you try this, you'll find that sometimes it works just fine -- and
sometimes it doesn't -- and Mathematica gives you no warning
anywhere in the elementary discussions of /. or -> or I that you
shouldn't do this, or why you shouldn't.
So don't do it this way (but don't expect a lot of sympathy from
this group for people doing elementary phasor analyses like
you're doing, who are misled by this line of thinking).