Result of z+conj(z) and z*conj(z) with z complex by default

Hello everyone. Is it possible to get z+conj(z)=2*Re(z) and z*conj(z)=(abs(z))^2 without defining z=a+1i*b? I tried to wrote:

close all
clear all
syms z         %z complex by default
z+conj(z)      %result z+conj(z)
z*conj(z)      %result z*conj(z)

Thank you in advance.

[KSSV]

How syms z will be default complex?

Answer 1

[John D'Errico]

Absolutely impossible. ;)

But why not try it?

syms z
simplify(z+conj(z))
ans =
2*real(z)

simplify(z*conj(z))
ans =
abs(z)^2

Surely it is always worth a try?