Where is the world of Imaginary numbers? Complex numbers have two parts, Real and Imaginary parts.
Real world is base of Real numbers.
but 
where is (or what is) the world of Imaginary numbers?

Complex numbers can be thought of as 'rotation numbers'. Real matrices with complex eigenvalues always involve some sort of rotation. Multiplying two complex numbers composes their rotations and multiplies their lengths. They find frequent use with alternating current which fluctuates periodically. Also, $e^{ix}=\cos x+i \sin x$, parametrizing a circle. 
