and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
You know how when you first learned about addition and subtraction, you learned that you can only take a smaller number from a bigger number? That is, 5 – 3 is 2, but 3 – 5 is not allowed. Because if you have a basket with three apples in it, it doesn’t make any sense to take more than three apples out of that basket.
But then, later on, you learned that, actually, you *can* take a bigger number from a smaller number, you just end up with a *negative* number. And while a basket can’t contain a negative number of apples, negative numbers can still be useful for describing things like debt, or downward motion, or a bunch of other things.
There’s another rule in math that says you can’t take the square root of a negative number. That’s because when you square a negative number, you get a positive number, so no number, positive or negative, can be squared to get a negative number.
But, just like with subtraction and negative numbers, it actually is possible to take the square root of a negative number. It’s just that the answer is a new *type* of number, like how negative numbers were a new type of number.
These numbers are called imaginary numbers for historical reasons, but they’re no more imaginary than negative numbers. Again, a basket can’t contain an imaginary number of apples, but imaginary numbers are still useful for describing real life things like electrical current or quantum mechanics.
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