He probably means the algebraic structure of a field. "A field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do."[0]

You might be tempted to think of complex numbers as "just" being 2-dimensional real vectors (x, y). Looks pretty similar to how you can plot a complex number a + ib at point (a, b) on a 2D plane. But importantly, division is defined on a field, which is not necessarily true for vectors. For any complex number (except 0), you can find another complex number that multiplies with it to give 1, the multiplicative identity.

You _can_ think of complex numbers as being "made of" real numbers though. a and b above are just real numbers. Complex numbers are the two-dimensional normed division algebra over the reals[1].

[0] https://en.wikipedia.org/wiki/Field_(mathematics) [1] https://ncatlab.org/nlab/show/normed+division+algebra