Physical meaning of the addition of Re[z] and Im[z], given Re[z] and Im[z] satisfy KK relation.

Question

Recently I came into an expression of Re[z] + Im[z], where, Re[z] and Im[z] satisfy the Kramers–Kronig relations. Wiki shows a page explaining like this, but the real part and imaginary part are separate. I'm just wondering if there is anyone who ever came across an expression like Re[z] + Im[z]. Any comment is appreciated.

Comments

It must be a typo; the imaginary unit $i$ is missing at Im(z).

---

Can you give a reference to where this happend?

---

@Dilaton, @VladimirKalitvianski, thanks very much for your comments.

No, there is no missing i here.

It's just a hypothesis from a combination of several articles. For example, please refer to figure 1 in this one and equation 2.3 in this one.