Complex Analysis using Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg52621] Complex Analysis using Mathematica
• From: "Pratik Desai" <pdesai1 at umbc.edu>
• Date: Sat, 4 Dec 2004 04:08:00 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Here we go again,

I have to define a complex function
So I go through this procedure to define that the variables are  really "real"

TagSet[p, Im[p], 0];
TagSet[a, Im[a], 0];
TagSet[b, Im[b], 0];
TagSet[p, Re[p], p];
TagSet[a, Re[a], a];
TagSet[b, Re[b], b];
lamda = a + I*b
z = ComplexExpand[lamda*p]
x=Re[z]
y=Im[z]
TagSet[u, Im[u[x, y]], 0];
TagSet[v, Im[v[x, y]], 0];
TagSet[x, Re[x], x];
TagSet[y, Re[y], y];
TagSet[u, Re[u[x, y]], u[x, y]];
TagSet[v, Re[v[x, y]], v[x, y]];

Then I define my actual function

u1 = TrigToExp[Sinh[z]] (*By this time I have realized that
Mathematica or for that matter most of the CAS work better with
exponentials when it comes to complex analysis*)

u[x, y] = Re[u1]
v[x, y] = Im[u1]

The problem I face is that the software is not able to identify x and y
as I have defined above. May be I am making a trivial mistake. Please