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When solving equations (of e.g. 2nd grade) the discriminant is part of a squareroot.

A square root of 'x' is the number that multiplied y itself equals 'x'.

Any number we can think of - when multiplied by itself (squared) gives a positive number. (even negative number - e.g. -2*-2 = 4)

So we cannot think of a number which square is negative.

Then sq.root(-1) has no answer - no number squared gives -1.

Therefore the number that equals sq.root(-1) is imaginary.

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Q: Why does a negative discriminant yield imaginary numbers?
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