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...Week complex numbers richard earl mathematical institute oxford ox lb november abstract cartesian and polar form of a number the argand diagram roots unity relation ship between exponential trigonometric functions geometry need for all you will know that two quadratic equation ax bx c are x b ac solving equations is something mathematicians have been able to do since time babylonians when then these real distinct graphically they where curve y cuts axis we one root just touches here but what happens there no solutions as squares give negative from graphical point view lies entirely above or below repeated it only comparatively recently comfortable with during renaissance would considered unsolvable its called imaginary term was rst used by french mathematician rene descartes whilst he known more philosopher made many important contributions mathematics helped found co ordinate hence naming ordinates if imagine exist behaves adds multiplies much same other can be written in arerealnumbe...