Imaginary Numbers are "Real"

April 9, 2013

 

     In my classroom we have been discussing imaginary numbers. We can solve equations like this all day long:   The answers are 3 and -3. But suppose some wiseguy puts in a teensy, tiny minus sign:  Uh oh. This question makes most people cringe the first time they see it. 

 

     It seems crazy, just like negatives, zero, and irrationals must have seemed crazy at first. There's no "real" meaning to this question, right? Wrong. So-called "imaginary numbers" are as normal as every other number: they're a tool to describe the world. Let's assume some number i exists where:

That is, you multiply i by itself to get -1. What happens now? This makes math easier and more elegant. 

 

      New, brain-twisting concepts are hard and they don't make sense immediately, but strange concepts can still be useful.

Mrs. Brandyberry

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