If Jimmy has negative seven cookies and eats the square root of them, does he have more than zero left?
This question was, of course, primarily designed to make fun of the limited number of applications that exist for some of the most interesting pieces of mathematics. Even the few applications that do exist for imaginary numbers are rather esoteric and obscure. But it is no surprise that departure from real numbers makes applicability in the real world sparse.
However, for those of you quixotics who, like me, don’t care so much about the real world, I have decided to write a brief discussion of the topic. The question is: Is i root seven positive or negative? Most people will want to say it is positive, but consider the following:
The fact that i = –i might leave some readers confused. There are many ways of looking at this, but here’s the one that I prefer: i is neither negative nor positive, it is imaginary, and only real numbers can be compared with zero. When we say “negative i,” what we really mean is “i times negative one”. i can have a real coefficient, but, being imaginary, has no sign. Therefore, the number of cookies Jimmy had is a truly matter of philosophical inquiry.
A friend of mine put it well: “He has something other than zero cookies, but really, he has nothing–except in his imagination”.
Therefore, the answer to the question posed earlier (Is i root seven positive or negative?) is no.