What are imaginary numbers?? Why can’t the square root of a negative be real?
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All of the real numbers can be placed on a line. 5 is bigger than 1, -6 is smaller than -3… But if I asked you to place an imaginary number on this line, you couldn’t right?
That’s why it is “imaginary”. No real number can be multiplied by itself so that it produces a negative number, because multiplying 2 positives (4 * 4 = 16) = positive and multiplying 2 negatives (-4 * -4 = 16) = positive. So if we want a number which, when multiplied by itself, equals a negative, we cannot find a real number, we needed to invent one: i.
We chose to define i such that i² = -1. We cannot place i on our line of real numbers -> it is imaginary.
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