SHOULD WE USE COMPLEX NUMBERS

The concept of complex numbers was introduced by Euler, when he tried to solve the equation x^2 + 1 = 0. But is there any physical system where this equation is fulfilled? The answer is no. If we rewrite the equation as x^2 = -1, still then it will not lead to mathematics or physics because squaring is done with not only the numbers, but also signs. Two negative signs square up to positive as per the mathematical rules. Then how can x^2 be equal to -1? Further if i denotes square root of -1, what about the equations x^2 + 2 = 0, x^2 + 3 = 0, x^2 + 5 = 0, x^2 + 7 = 0, etc.? Why do not we invent suitable terms to explain square roots of -2,-3,-5,-7, etc? In that case, the required symbols will be infinite and doing mathematics will be impossible. For this reason, complex numbers cannot be used in computer programming. Some people say complex numbers include real numbers and more. In that case, dream should be used instead of observation, because dream includes what we observe and more. May be for that reason modern scientists are including dream with observation to formulate theories based on extra-dimensions, strings, foams, chamelions, axions, gravitons, sparticles, bare mass, bare charge, dark matter, dark energy, expansion of the universe (even though it is not observed in less than galactic scales and we observe ), inflation, etc. But their dream costs humanity huge costs, which could otherwise have been enough to eradicate poverty from the world. Should dreams get primacy over real sufferings of the world?