For those who don't know what a complex number is, in simple terms, a complex number is the square root of a negative number! For example, the square root of -1 is called a complex number. Those numbers appear in laws describing real-world phenomena. Hence my question, how can we rationalize the fact that complex numbers exist?
I have some intuition about how to work with rational or real numbers, but complex numbers appear to be indistinguishable from magic! Why do we think relying on such numbers for physical theories is fine? Isn't this a huge problem, that most Physics is based on this?
** End of question by NoChance **
Comment: This is somewhat inaccurate. ... "Complex number"-s are the 'superset' of real numbers: they 'expand' the set of real numbers to 'include' the set of 'imaginary' numbers. .. Any positive number in the real number system has two square roots - positive and negative square root (I'm neglecting zero here because it is neither positive nor negative, but a number which is itself regardless of addition (by itself) or multiplication). But what about negative numbers? -- To help 'complete' this system of having square roots for ALL (up-until-then, known) numbers the concept of the imaginary number "&i$" was introduced [Reference: http://jeff560.tripod.com/i.html]: defined as the "number", when multiplied to itself, gives the number -1. Afterwards, the rest is - as they say - history! ... So, by definition a complex number is defined as a 'number' of the form $a + bi$ where $a$, $b$ $\in$ $\mathbb{R}$ [the set of all real numbers]. ... (Such numbers, considered by many, are their own mathematical objects - not the same as real numbers, but subtly related to them (via some very deep properties of mathematics which I don't know)). They are no less "numbers" than the "reals" or "rationals". ... Plus, from philosophy: what we call 'reality' can only be known from our experience(s) of it through our five senses: without them there is NO way for us to know anything of "reality" (you would have to ask a professor of philosophy why.. I don't really know why). Therefore, what we call 'intuitive' may / may not readily reflect the "ontological" nature of 'physical "reality"': hence, there are many [mathematical] concepts and constructs used in physics that are not readily humanly 'intuitive' [something to do with "positivism" 'n such.. again, I couldn't tell you what] - but, they are nonetheless central to investigating the measurable and experimentally-amenable features of our 'world'.]