FYI, this link [PDF] https://personalpages.manchester.ac.uk/staff/paul.johnson-2/... contains the peculiar statement "Over the next few years, FORTRAN II would also add support for the DOUBLE PRECISION and COMPLEX data types."
At face value, that statement implies complex numbers came later but before FORTRAN III, which also implies a point release (FORTRAN II was released in 1958). Moreover, I read somewhere that FORTRAN III had it but it wasn't widely released. Likely then that FORTRAN IV was the first widely released version with complex numbers. As it was released in 1961, we should assume then that this was the likely date.