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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.
Why is a real number is a component of the real number system?
It would be a bit stupid to call a system the real number system if real numbers were not a part of it!
How are complex numbers and real numbers related?
Complex numbers extend the concept of real numbers by introducing an imaginary unit, denoted as "i." Real numbers can be considered a subset of complex numbers with the imaginary part equal to zero. Complex numbers include both a real and imaginary component, allowing for operations like addition, subtraction, multiplication, and division.
Why are imaginary numbers used in electronic systems control systems and physics?
Mathematics is beautiful in itself. Back in the 1700s and later, mathematicians studied "imaginary" numbers (numbers that involve a factor of the square root of -1) knowing that they didn't describe anything "real", the way "real numbers" do. But when beauty can be melded to practicality, things get REALLY interesting. It turns out that you can use imaginary numbers and "complex numbers" (which have a "real" component and an "imaginary" component) to describe the way radiation and electromagnetic fields behave.
Are natural numbers real numbers?
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
