NOTE: Read the Number Sets Notes page before starting here.
"Given that x is a real number, how many values of x fulfil the equation:
$x^2 = -16$
Answer:
No real numbers can fulfil this equation.
We are looking for a number that when squared, is the absolute value of -16, and then maybe we could make it negative. The only 2 possible candidates, 4 and -4, both do not square to -16, they both square to 16. This is because positive times positive is positive, and negative times negative is positive. Therefore, it is impossible to describe the square root of a negative number with a real integer.
This is where complex and imaginary numbers come in.
