What are imaginary numbers?? Why can’t the square root of a negative be real?
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The square root of a negative number can’t be a Real number because no Real number times itself equals a negative number. Any positive Real number times itself is a positive Real number and any negative Real number times itself is is also a positive Real number (and 0 * 0 is 0).
But, a long time ago, mathematicians were trying to solve certain kinds of problems and they realized that you had to be able to take the square root of a negative number, albeit temporarily, to work out these solutions. So apparently it was possible to do this and not break the rules of mathematics.
Since this was a new discovery that went against the common understanding of Mathematics at the time, there was some resistance and criticism to accepting these new kinds of numbers. Some mathematicians that were critical of the concept gave these numbers derogatory names, like “imaginary” and “useless.” Unfortunately, these ill-sounding names stuck.
So an Imaginary number is a number that, when multiplied by itself *does* equal a negative Real number, something Real numbers can’t do. We define the base imaginary number, *i*, such that i^(2) = -1 and all other imaginary numbers are multiples of i.
But don’t let the name confuse you, Imaginary numbers are just as “real” as Real numbers.
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