Why do we call imaginary numbers "imaginary numbers"? As far as I can tell, there's nothing really imaginary about them. They exist. They're used all the time. What makes them so "imaginary"?
Those numbers were once poorly understood and regarded by some as fictitious.The use of imaginary numbers was not widely accepted by many. It was left to Euler and others to use them. Euler, in his Introduction to Algebra, wrote the following:
Because all conceivable numbers are either greater than zero or less than 0 or equal to 0, then it is clear that the square roots of negative numbers cannot be included among the possible numbers [real numbers]. Consequently we must say that these are impossible numbers. And this circumstance leads us to the concept of such number, which by their nature are impossible, and ordinarily are called imaginary or fancied numbers, because they exist only in imagination.
In short, it is a matter of acceptance of or the lack of it which gave them the name.
Mathematicians thought up an answer to the square root of -1, and they simply "imagined" a soultion, hence imaginary numbers. they found out it could be very useful, and kept it that way. the name, however, has stuck.