Question

Sa se rezolve in multimea numerelor complexe ecuatia $z^{2}=-4$
Vreau cat mai detaliat multumesc

Answer 1

[tex] z^{2} =(-1)*4=i^2*4 \\ \\ z=+_- \sqrt{4i^2} =+_-2i \\ \\ z_1=2i \\ \\ z_2=-2i[/tex]

Answer 2

[tex]z^2=-4\\ z^2+4=0\\ z^2-i^2\cdot2^2=0\\ z^2-(2i)^2=0\\ (z-2i)(z+2i)=0\\ z-2i=0\text{ sau } z+2i=0\\ z_1=2i,\ z_2=-2i\\ S=\{-2i,2i\} [/tex]