Mathematicians once turned up their noses at imaginary numbers. But complex analysis actually simplifies math and physics.

If a quadratic equation can be factorised ... It is not possible to find the square root of a negative number, so the equation has no solutions. The graph of \(y = x^2 + 2x + 5\) does not cross ...

If a quadratic equation can be factorised ... It is not possible to find the square root of a negative number, so the equation has no solutions. The graph of \(y = x^2 + 2x + 5\) does not cross ...

Maybe your high school teacher didn’t want to deal with the issue of what happens when (b 2 - 4ac) – the expression under the square root in the quadratic formula – is negative. They might ...

However, if you are willing to believe in the existence of square roots of negative numbers, you will get solutions to a whole new set of quadratic equations. In fact, a whole amazing and useful ...