Question

determine o complexo z sabendo que 3. z2=9+12i

Answer 1

sea $\displaystyle z=a+b i\Longrightarrow z^2 =a^2-b^2+2abi\\ \\ \begin{cases} a^2-b^2=9\\ ab=6 \end{cases}\\ \\ b=\frac{6}{a}\Longrightarrow a^2-\frac{36}{a^2}=9\\ \\ a^4-9a^2-36=0\\ \\ (a^2-12)(a^2+3)=0\\ \\ a\in\left\{-2\sqrt{3},2\sqrt{3},-\sqrt{3}i,\sqrt{3}i\right\}\\ \\ \boxed{z\in\left\{-2\sqrt{3}-\sqrt3 i,2\sqrt{3}+\sqrt3i,-2\sqrt{3}+\sqrt3i, -2\sqrt{3}-\sqrt3i \right\}}$