and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
Of the numbers you’re used to, like 1 or 2 or -2.7, none of them can be multiplied by themselves to get a negative number. A negative times a negative is a positive, and a positive times a positive is a positive.
So, what times itself is negative? None of the “real” numbers that you’re used to, that’s for sure. So, let’s make up a number and cal it “i”. This number has no “real” value that you can write down, so we’re stuck calling it “i” forever. But, we can say that i times itself is -1. Or, put another way, i is the square root of -1.
There are a lot of times that it can be useful to find the square root of negative numbers, for instance in differential equations it shows up a lot, and can suggest periodic functions (like sine and cosine).
A lot of this comes from the fact that we can use real and imaginary numbers to represent two dimensions in “one number”. Something like 2+3i corresponds to (2,3) but we can treat it as one number, streamlining math.
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