Răspuns:
nu ECUATIA, ci O ecuatie pt ca sunt o infinitate
Explicație pas cu pas:
conf. teoremei fundamentale a algebrei, o scriem sub forma algebrica
are coeficienti complecsi, datorita factuluica rad.complexe nu sunt conjgate
[tex]\displaystyle\bf\\Explicatii:\\O~ecuatie~la~care~cunosc~solutiile~se~scrie~cu~formula:\\\\(x-x_1)(x-x_2)(x-x_3)=0~~pentru~Real\\\\(z-z_1)(z-z_2)(z-z_3)=0~~pentru~complex.\\\\Rezolvare:\\\\(z-z_1)(z-z_2)(z-z_3)=0\\\\(z-1)(z-i)(z-(1-i))=0\\\\Desfacem~primele~2~paranteze.\\\\(z^2-iz-1z+1\times i)(z-(1-i))=0\\\\(z^2-(1+i)z+i)(z-(1-i))=0[/tex]
.
[tex]\displaystyle\bf\\Desfacem~parantezele~ramase.\\\\z^3-(1+i)z^2+iz-(1-i)z^2+(1-i)(1+i)z -i(1-i)=0\\\\Facem~reducerile:\\\\z^3-[(1+i)+(1-i)]z^2+[i+(1-i)(1+i)]z -i(1-i)=0\\\\z^3-[1+i+1-i]z^2+[i+(1^2-i^2)]z+(-i+i^2)=0\\\\z^3-2z^2+[i+(1-(-1))]z+(-i-1)=0\\\\z^3-2z^2+[i+(1+1)]z-(1+i)=0\\\\\boxed{\bf z^3-2z^2+(2+i)z-(1+i)=0}[/tex]
