and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
Squaring a number (x^(2)) means taking a number x and multiplying by itself. So 3^(2) is `3 * 3 = 9`. The square root of a number is the opposite, find what number multiplied by itself will equal it. The number 9 for example has a square root of 3, but also -3. `-3 * -3` gives you 9. Imaginary numbers kick in when you want the square root of a negative number.
What’s the square root of -9?
It’s not 3 since that gives 9, it’s not -3 since that also gives 9. We need some way of breaking out that negative. What we can say is it’s the square root of 9 * the square root of -1 (i) so our answer is 3i. We use i to represent the square root of -1. It’s imaginary.
Now to the real question, what can we do with that? Well, you might have some formulas that use square roots and the values might end up negative. That might be OK though if you can eliminate the i. So lets say you end up with:
`x = (2 + 3i)(2 – 3i)` which becomes
`x = 4 + 6i – 6i -9i`^(2) which becomes
`x = 4 – 9i`^(2)
Now we’ve already said i is the square root of -1. If you square that, that means you have the real -1!
`x = 4 – (9 * -1)`
`x = 13`
Basically even if you need imaginary numbers, your algorithms might be able to get rid of them or make them not matter BUT it allows you to do the math on paper.
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