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The square of any real number cannot be negative. However, there are equations whose solutions require the square root of negative numbers. The real number system was extended to the set of complex number to allow such operations. In some ways, this is analogous to the set of integers being extended to the set of rational numbers to allow division (when the denominator was not a factor of the numerator), or the set of rational numbers being extended to real numbers to allow square (and other) roots.
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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.
Could anyone list numbers not in the set of complex numbers?
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
What are the kinds of complex numbers?
Complex numbers include real numbers, pure imaginary numbers, and the combination of those two.
Do the complex numbers for a group under binary operation ' plus '?
Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.
