Is there a name for set of numbers $\mathbb{Q} + i\mathbb{Q}$

Question

Just out of curiosity is there a standard name for a set of numbers $\mathbb{Q} + i\mathbb{Q}$ where $\mathbb{Q}$ stands for set of rational numbers, $i$ your complex number.

Answer 1

These are called Gaussian rationals.

This is a somewhat rare term in my experience. Yet the term Gaussian integers for $a+ib$ with integers $a,b$ is quite common.

The former is the quotient field of the latter so the term certainly makes sense.

Answer 2

They are called Gaussian rational numbers.

Answer 3

At the very least, there's definitely more convenient notation: the extension field $\mathbb{Q}(i)$ of $\mathbb{Q}$ can be thought of as a $2$-dimensional vector space over $\mathbb{Q}$ spanned by the basis vectors $1$ and $i$. That is, $\mathbb{Q}(i) = \{x + iy \ | \ x, y \in \mathbb{Q} \} = \mathbb{Q} + i\mathbb{Q}$.