Why is the square root of -4 an imaginary number instead of -2?
In: Mathematics
These two questions are the same:
– What is the square root of -4?
– What number, when multiplied by itself, is -4?
If you multiply -2 by -2, you get 4 (that is, positive 4).
That’s why it’s not -2.
Why does it have to be a different kind of number? Well:
– Zero times zero is zero. It can’t be zero.
– Positive times positive is positive. It can’t be positive.
– Negative times negative is negative. It can’t be negative.
So at some point, someone said “What if invent had something that, when multiplied by itself, gives us a negative result?” That’s basically where imaginary numbers come from.
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