Multimea numerelor complexe C ...us pentru zzz-1z-1z1, z!, z-1 element invers pentru zz1z2z3z1z2z1z3, z1,z2,z3! distributivitatea inmultirii fata de adunarez1z2z3z1z3z2z3, z1,z2,z3! distributivitatea inmultirii fata de adunare.Forma algebrica a numarului complex zxiy Rez x partea realaImzy coeficientul partii imaginareiy parte imaginarai unitate imaginarai2-1z1z2x1i y1x2iy2x1x2iy1y2 adunareaz1z2x1iy1x2iy2x1x2-y1y2ix1y2x2y1 inmultirea.Egalitatea a doua numere complexez1x1i y1 x1,y1, z2x2iy2 x2,y2, z1z2 x1x2 si y1y2Conjugatul numarului complex z EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 .Modulul unui numar complex zxiy EMBED Equation.3 !.z1z2z1z2 EMBED Equation.3 .Puterile lui i EMBED Equation.3 Reprezentarea geometrica a numerelor complexezxiyx,y, x,y! i se asociaza punctul Mx,yM se numeste imaginea geometrica a numarului complex xiyxiy se numeste afixul punctului MaAOM EMBED Equation.3 OM EMBED Equation.3 .Forma trigonometrica a numerelor complexe zrcos t i sin tOM EMBED Equation.3 - r raza polara a imaginii lui zxr cos t, yr sin t, tg t EMBED Equation.3 arg zt argument redus al lui zArg zIt targ z 2k, k!SIt tt2k, k!S argumentul lui zz1r1cos t1 i sin t1, z2r2cos t2 i sin t2 ! z1 z2r1 r2 icost1 t2 i sin t1 t2s - inmultireazrcos t i sin t ! znrn cos nt i sin nt ridicarea la puterecos t i sin tn cos nt i sin nt formula lui Moivrez1r1cos t1 i sin t1, z2r2cos t2 i sin t2 ! EMBED Equation.3 icost1- t2 i sin t1- t2s - impartireaznrcos t i sin t ! zk EMBED Equation.3 , kI0, 1, , n-1S- radacina de ordinul n. Rezolvarea ecuatiei de gradul II cu coeficienti reali ax2bxc0 a, b, cR, a0, b2-4ac, cazul EMBED Equation.3 - x1, x2 sunt radacini complexe conjugateEcuatii binome znc0, c !, n!, ne2 se scrie numarul -c sub forma trigonometrica!znrcos ti sin t!zk EMBED Equation.3 , kI0, 1, , n-1S EMBED PBrush iBFJLNRTZt0268RTVXafhnpvxaaaaajCJ56CJCJHjICJCJOJaQ Ja5CJ5CJOJaQJa5CJmHsHCJPJLi6JiPŕZ4faaFKaaaaaaaaaaa abdhjnptvxzŕai68iBDFJLPRVXZ ŕiaaCJHjCJCJOJaQJajICJCJHCJViBFHLNTVXZabdhjnptvzai DFŕ02 jICJjCJCJHCJH CJCJOJaQJaCJHOJaQJaVXŕpraFxaaaaBIfaaaaaFKIfaaaaIfaa aaFTIfaaaaIfaaaaaaaaaFKaa28iBHJRTVXtablnprvxzŕa.046 iBFHJLNRTXZdfjlr... Download |