The world isn't "real" (people rightfully find imaginary numbers a bad name, but real is equally bad). Complex numbers show up all over in physics. As to why, who knows? We just model what nature does, and it turns out that complex numbers form a very simple (relatively speaking) accurate model.
> The fact that an n-qubit quantum computing system is significantly powerful than classical system because of 2^n states. But, a classical system with n-bits will also have 2^n states, isn't it?
A n-bit pure quantum state can be fully described using 2^n complex numbers, and thus have 2^(n+1) degrees of freedom, which is a vastly bigger space than n bits. While quantum amplitudes are distinctly not probabilities (and more powerful), you can think of the difference in state space roughly by comparing the difference of storing one n-bit number v.s. storing one specific probability distribution over all n-bit numbers.