Those are all valid ways of conceptualizing those sets, but I don't think it changes the point I was making. The real number 3 doesn't need to be "converted" to a complex number to be added to 2+i. 3 is always both a real number and a complex number, which may be represented as either 3 or 3+0*i, and either way gives 5+i when added to 2+i. All the latter notation really does is clarifies what domain you're currently working in, and even so, I've never seen anyone write it out explicitly.
Type conversion is more like if you had the written number 3 and a picture of the point 5 on a number line and someone told you to add them. Naturally, you would write 5 as a number first, because you don't have a useful way to add a number and a picture. But this doesn't change the results of adding the quantities 3 and 5; it's purely an artifact of the way the information was presented to you.
Type conversion is more like if you had the written number 3 and a picture of the point 5 on a number line and someone told you to add them. Naturally, you would write 5 as a number first, because you don't have a useful way to add a number and a picture. But this doesn't change the results of adding the quantities 3 and 5; it's purely an artifact of the way the information was presented to you.