Why is the square root of -4 an imaginary number instead of -2?
In: Mathematics
The way my maths teacher described it to me is that if you take a set of axes and draw a 2×2 square in the top right quadrant its area is 4. And if you mirror it diagonally into the lower left quadrant it’s -2 x -2. But it’s area is the same as the first square you drew. So the areas are both 4. Meaning the square of a negative must be positive as well. Therefore in order to have the square of a number be a negative we have to create a new world where the root could be negative in order to get on and deal with the rest of the problem. Hence why we refer to it as an imaginary number.
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