I don't think so. But real numbers are complex.

ℝ∈ℂ

"real" is non-sensical when applied to concepts. Numbers are concepts. Their reality or unreality is undefined.

Positive integers, negative numbers, imaginary numbers, complex numbers, ... all just concepts, all equally real or unreal or IMHO neither.

i think its more that there aren't actually any real numbers, they're all basically imaginary