I saw in LaTeX that typing \Re gives '$\Re$', and typing \Im gives '$\Im$', and when I searched online, I found that "\Re is the LaTeX symbol for the real function $\Re$." on some website, so I assume that the same is true for \Im for "the complex function $\Im$".
But what are those functions? Are they the functions $\text{Re}(\>)$ and $\text{Im}(\>)$ defined on $\mathbb{C}$?
Best Answer
Based on DHMO's comment above:
They are notations for the same things:
$\forall z \in \mathbb{C}:$ $\text{Re}(z) \equiv \Re (z)$, the real part of $z$, $\text{Im}(z) \equiv \Im (z)$, the imaginary part of $z$