The Need for Complex Numbers

The general solution of the quadratic equationisandIfthenandare distinct real numbers.and can be plotted on the- axis, abd the graphwill pass though the points andIfthenand the graphjust touches the– axis but does not cross it. Ifthe m to find x-1 and x-2 we must take the square root of a negative number.andare not real numbers and cannot be plotted on the – axis. The graph does not cross the– axis, butandare still solutions to

The square root of a negative number is said to be 'complex' and labelled with the letter:andComplex numbers have many uses, in geometry, electricity, quantum mechanics, trigonometry, number theory...

Example: Ifthenand