Question

Z^3=-8
Rezolvati in multimea nr complexe

Answer 1

[tex]z^3=-8\\ z^3+8=0\\ (z+2)(z^2-2z+4)=0\\ i)z+2=0\Rightarrow z_1=-2\\ ii)z^2-2z+4=0\\ \Delta=4-16=-12\Rightarrow \sqrt{\Delta} =2i\sqrt{3}\\ z_{2,3}=\dfrac{2\pm 2i\sqrt3}{2}=1\pm i\sqrt{3}\\ S:z\in \{-2, 1\pm i\sqrt3 \}[/tex]