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...Complex numbers tsogtgerelgantumur contents brief history and introduction axioms models of algebra geometry appendix a the real number system thesquareofarealnumberisalwaysnonnegative i e negative is never square however it turns out that one can extend concept to include objects other than so are squares those hypothetical roughly speaking this how were discovered as far recorded goes gerolamo cardano was rst person encounter explicitly in his ars magna considers equation x if we apply usual solution formula for quadratic equations solutions get now writes ignoring mental tortures involved check there seems be some sense which really shows calculation but dismisses immediately by saying useless next step taken rafael bombelli sort motivation study he cubic px q with p applies or rather an approach equivalent had been described s thus gives date february makes guess andveries light becomes since whatisinteresting here intermediate calculations leading involve roots at time no way know...