Complex numbers are numbers of the form (x + yi) where x and y are real numbers and i is the imaginary square root of -1.
Any collection of such numbers is a set of complex numbers.
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Elements of the set C denote complex numbers.
The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".
No difference. The set of complex numbers includes the set of imaginary numbers.
The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.
The set of Real NumbersThe set of Imaginary Numbers