Boy surface parameterization confusion

Question

I'm looking at equations 10, 11 and 12 here. What do the letters I and R represent in these equations?

Answer 1

This notation is read as, I=Imaginary and R=Real.

Answer 2

Let $z\in\mathbb{C}$, where $\mathbb{C}$ is the set of complex numbers.

Any $z\in\mathbb{C}$ can be represented as

$$z=x+iy$$

where $x,y\in\mathbb{R}$.

We define $\mathcal{Im}(z)$ or just $\mathcal{I}(z)$ to be the imaginary part of $z$, thus

$$\mathcal{Im}(z)=\mathcal{I}(z)=y$$

And we define $\mathcal{Re}(z)$ or just $\mathcal{R}(z)$ to be the imaginary part of $z$, thus

$$\mathcal{Re}(z)=\mathcal{R}(z)=x$$