Date: Mar 3, 2013 2:21 AM
Author: Andrzej Kozlowski
Subject: Re: Conjugate


On 2 Mar 2013, at 09:46, =E9=81 =E5=B1=B1=E8=81=A1=E4=B8=80 =
<st.merl.ebina@gmail.com> wrote:

> I executed following inputs:
> Exit[]
> Element[{A, B}, Complexes];
> Conjugate[A + B] == Conjugate[A] + Conjugate[B]
> I expected "True" on the last input, but Mathematica's output was:
> Conjugate[A + B] == Conjugate[A] + Conjugate[B]
> Why didnt Mathematica answer "True"?
> Thanks.
>


Because instead of learning how Mathematica works you are guessing and
all your guesses are completely wrong. Since your first command does
nothing at all and neither does the second one, it is not very
surprising that Mathematica just returns back your code (if you had not
put the semicolon after your second input you would have got that back
too).
It's like trying to use a chainsaw the way one would use an axe and then
being surprised that it's so ineffective.

You can verify that this trivial identity holds by:

FullSimplify[Conjugate[a + b] == Conjugate[a] + Conjugate[b]]

True

or

ComplexExpand[Conjugate[a + b] - Conjugate[a] - Conjugate[b]]

0

but to find out what that means you will have to look at the
documentation yourself.