Why does the ABS function on symbolic variables not give the real and imaginary parts separately in the Symbolic Math Toolbox 5.5 (R2010b)?

Following is the reproduction code:

syms x y real

syms z complex

z=x+i*y;

abs(z);

This returns abs(x + y*i), instead of (x^2 + y^2)^(1/2).

Answer 1

[MathWorks Support Team]

The ability to do so has been incorporated in Release 2012a (R2012a) using the REWRITE function which was introduced in this release. The following code gives the desired result:

syms x y real 

z = x + i*y; 

a = abs(z); 

rewrite(a,'sqrt')

For previous product releases, read below for possible workarounds:

The ability to separate real and imaginary parts separately using ABS is not available in the Symbolic Math Toolbox.

As a workaround, you could use the MuPAD function RECTFORM as follows:

syms x y real;

z = x + i*y;

feval(symengine, 'rectform', abs(z))

Note that MuPAD assumes variables to be complex if not declared to

be real. Hence the need to use the REAL keyword.

Another possible workaround is as follows:

SIMPLIFY can be used to get the desired result. The example code is as follows:

syms x y real 

z = x + i*y; 

abs(z)

simplify(abs(z))

[Paul]

Can you post some code showing your concern? Is the following not what you expect?

syms x y real
z = 1/(x + 1i*y);
rewrite(abs(z),'sqrt')

ans =