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...Complex numbers in geometry sebastian jeon december the plane denitions i assume familiarity with most if not all of following some knowledge linear algebra is also recommended but required subsequently let be imaginary unit satisfying dene set num bers c z a bi b r where real part and magnitude given conjugate will implying property as an exercise show that w zw every can expressed cos isin for angle or alternatively ei this referred to argument lastly any number zn n th root unity k it easily veried these take form e applications assigns point such p cartesian coordinates assigned counterpart xy axes are respectively from denition similarity between should evident consequently representation corresponds polar throughout lecture lowercase letter correspond co ordinate ax unless otherwise noted verify reection over axis transformations geometrically order nd sum two one may simply perform vector head tail addition multiplication slightly more interesting map spiral composition dilation...