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Real numbers are a proper subset of complex numbers. In fact each complex number, z, can be represented as z = x +iy where x and y are real numbers and i is the imaginary square root of -1.
Thus the set of complex numbers is the Cartesian product of two sets of real numbers. That is, C = R x R where C is the set of complex numbers and R is the set of real numbers. Limitations of this browser prevent me from writing that in a mathematically precise and more helpful fashion.
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What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary numbers.
What is the difference between a complex number and real number system?
Graphically the difference is quite clear: the real numbers can be put on a line, the so-called number-line; while complex numbers are represented as points on a plane. A complex number is made up of two parts, like a vector in two dimensions.
What is the relation of complex numbers to real numbers?
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
Is the difference between two real numbers a real number?
Yes, I can't think of any way that a real number minus another real number would be complex or purely imaginary. My answer is yes.
What is the Difference between an integer and a real number?
Integer numbers are a subset of real numbers. Real numbers may contain fractions.
