and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
So you’ve got the “natural numbers”. They go 0, 1, 2, 3 etc. People seem generally happy with those.
Then we discover some rules which apply to those numbers. 1+2=3. 6-4=2. Lots of other rules.
But what is 4-5? That question doesn’t have an answer in the “natural numbers”. But what mathematicians did was they said “Let’s pretend there is a number that answers that question”.
We call this made up number “negative 1”. What we discovered is that most of the rules of the “natural numbers” apply to these “negative numbers” – by pretending this number exists, we find that maths still works!
Then we came to a different problem – what is the square root of -1? Again mathematicians imagined a new number, which they called “i”. And again, they found that most of the rules still apply. Maths still works by pretending this number exists as well.
There are lots of usages of this number, but the key usage of it is it lets us deal with the square roots of negative numbers when they pop up. If it didn’t exist, then any square roots of negative numbers would break our equations. By “pretending” an answer exists, we can continue working through them, and end up with sensible solutions anyway. One such example is the cubic formula, where by continuing to work through the maths as though it makes sense, we can find sensible solutions.
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