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

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