Simplify symbolic division abs(Z)/Z

In a symbolic expression with syms Z complex, Matlab does not simplify simplify(abs(Z)^2/Z) to conj(Z) but it simplifies simplify(abs(Z)^2/conj(Z)) to Z. Is it possible to make sure that simplify(abs(Z)^2/Z) yields conj(Z)? I'm working with R2023b. Thanks!

Answer 1

[Torsten]

Use z*z' instead of abs(z)^2:

syms z 
u = z*z'/z

u = 

[Luciano Boglione]

Thank you for your suggestion. However, I get abs(Z)^2/Z as a result of a calculation on complex symbolic varialbles - then, I try simplify( expression that contains abs(Z)^2/Z ) but it doesn't simplify it. That's my issue!

[Torsten]

Then I think you are out of luck. Why do you want to simplify ? Just for optical reasons ?

This will work, but it's the sledge hammer:

syms z
u = abs(z)^2/z;
u = subs(u,abs(z)^2,z'*z)

u = 

Answer 2

[Walter Roberson]

syms z
syms zr zi real
u = abs(z)^2/z

u = 

us = simplify(subs(u, z, zr + 1i*zi))

us = 

After which you would need to substitute conj(z) for zr-zi*1i

However it is probably easiest to do something like

syms z
u = abs(z)^2/z + 5*z^2 - 3*z + 2

u = 

subs(u, abs(z)^2/z, conj(z))

ans = 

If you have something more complex, where you have the general pattern abs(EXPRESSION)^2/EXPRESSION then you could proceed by using mapSymType ... but it does get complicated if you have terms such as (x*abs(x + y)^2)/(y*(x + y)) then it can be complicated to properly detect a match.