The “opposite” of real numbers are (logically enough) called imaginary numbers. In particular, they are all non-zero multiples (real numbers) of the square root of -1, also called i, with the formula defined as follows:

The does not have a position on a number line; and no number can be squared to get -1. (If you square a positive number, the result is positive; if you square a negative number, the result is also a positive number.) Thus, in order to square a number to get a negative one, mathematicians invented the imaginary number i.