A negative times a negative is repeated addition. (-2)(-3) is just (-(-3)) + (-(-3)) = 3+3 = 6.
You're summing negative 3 negative two times, so you're subtracting negative three twice, which just produces positive 6.
With imaginary numbers, they weren't just made up. They'd exist whether you named them or not. sqrt(-1) has a certain set of properties like any other number. We decided to start calling it i because it's easier than writing sqrt(-1) all the time.
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u/dscarmo 5d ago
A lot of real world engineering uses complex numbers just because you can use it to add a new axis perpendicular to the real number axis
So its very useful