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 have ...

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 ...