Re: Imaginary numbers aren't real, but aren't real numbers imaginary too?

Yes.   All numbers are in our imagination.  So in that sense "real" numbers
are just as imaginary as "imaginary" numbers.   The term imaginary was
applied when it was noticed that these numbers are neither less than or
greater than zero.

The real numbers were pictured as being on an infinitely long line.  A point 
on
that line was thought as the middle of the line, and labelled as zero.
Positive
numbers were to the right of zero.  Negative numbers were to the left of 
zero.

Imaginary numbers could not be pictured as on the line at all.  Since nobody
knew, at the time, how to picture imaginary numbers, it made sense to call
them imaginary.

Later it was figured out that we could picture the imaginary numbers by
placing them on a line perpendicular to the real number line.  Another
infinitely long line perpendicular to the real number line goes through the
zero point.   So zero is the zero for both real numbers and for imaginary 
numbers.

George Gamow's  book talks a little bit about this representation of
imaginary numbers and also talks about adding imaginary numbers to real
numbers to make complex numbers.

Another important point is that the square root of -1 is still one unit away
from zero.  It is just that it is one unit away in the vertical or 
"imaginary"
direction.