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(1) Symbolic complex algebra in mathematica and (2) Dsolve


(1) I hope I am not correct about this.  I want to define a complex quantity

	z = x + I y

so that 

	Re[z] ==> x
	Im[z] ==> y
        Conjugate[z] ==> x - I y

etc.  Mathematica doesn't seem to know how to do this even after I define
x and y to be real by

	x/: RealQ[x] = True

(Of course, this does not change the head of x which is still Symbol.)   
Next I tried to define some transformation rules, but then I couldn't
find a way to specify the pattern variable to be of type real AND symbol.


(2) I want to solve a simple harmonic equation with boundary conditions:

DSolve[{x'[t] == y[t], y'[t] ==  k^2 x[t], y'[-h] == 0},{x[t],y[t]}, t]

But mathematica seems to ignore the boundary constraint.


Any wisdom?

P.S.  Originally I plan to use Mathematica to help me solve some
linear non-homogenous PDEs, but after a few hours playing witb it,
I am becoming increasingly frustrated with many of the simple things
it can't do.  Is that due to my insufficient knowledge of mathematica
or is that due to mathematica itself?




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