Question

Sa se rezolve ecuatia

z^2 = -2i

Answer 1

   
[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]