[tex]\displaystyle\\
z^2 = -2i\\
\text{z este un numar complex de forma: }\\
~~~~z=a+bi\\
\text{Rescriem ecuatia:}\\\\
(a+bi)^2=0 -bi\\\\
a^2 +2abi + (bi)^2=0-2i\\\\
a^2 +2abi -b^2 = 0 -2i\\\\
(a^2-b^2) + 2abi = 0 -2i\\\\
\text{Acum ecuatia se descompune in 2 ecuatii, }\\}
\left\{ {{a^2-b^2=0} \atop {2ab=-2}} \right\\\\
\left\{ {{a^2=b^2} \atop {ab=-1}} \right\\\\
\left\{ {{a=\pm b} \atop {ab=-1}} \right\\\\
\Longrightarrow a = \pm1 ~~\text{ si }~~b = \mp 1
[/tex]
[tex]\displaystyle\\
\texttt{Solutia 1:}\\
\boxed{\bf {{a=1} \atop {b=-1}} \right}\\\\
\texttt{Solutia 2:}\\
\boxed{\bf {{a=-1} \atop {b=1}} \right}[/tex]
