Numbers, Complex
The set of complex numbers includes all the numbers we commonly work with in school mathematics (whole numbers, fractions, decimals, square roots, etc.), plus many more numbers that are generally not encountered until the study of higher mathematics. Complex numbers were invented centuries ago in order to provide solutions to certain equations that previously had seemed impossible to solve.
Imagine trying to find a solution to x+ 6 = 4 but being able to look for a solution only in the set of whole numbers. This is impossible. However, if we expand our domain to all integers, - 2 provides a solution. Similarly, it is impossible to find a solution to 2x = 7 using only integers, but we can expand our domain to the set of rational numbers, and or 3.5 provides a solution. Now suppose you wanted to find a solution to x2 = 2 using only rational numbers. This, too, is impossible. However, the set of rational numbers can be expanded to create still another new set of numbers—the real numbers. Clearly, is one solution to the equation x2 = 2 because by definition the square root of any number multiplied by itself equals the number: .
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