\n
Resolu\u00e7\u00e3o<\/b><\/span><\/p>\nConsiderando $z = x + yi$, vem ${z^2} = \\left( {{x^2} – {y^2}} \\right) + 2xyi$.<\/p>\n
\n- \u00ad$$\\begin{array}{*{20}{l}}
\n{\\operatorname{Re} \\left( {{z^2}} \\right) = 0}& \\Leftrightarrow &{{x^2} – {y^2}=0} \\\\
\n{}& \\Leftrightarrow &{\\begin{array}{*{20}{c}}
\n{y = x}& \\vee &{y =\u00a0 – x}
\n\\end{array}}
\n\\end{array}$$<\/li>\n - \u00ad$$\\begin{array}{*{20}{l}}
\n{\\operatorname{Im} \\left( {{z^2}} \\right) = 2}& \\Leftrightarrow &{2xy = 2} \\\\
\n{}& \\Leftrightarrow &{y = \\frac{1}{x}}
\n\\end{array}$$<\/li>\n - \u00ad$$\\begin{array}{*{20}{l}}
\n{{z^2} = 2i}& \\Leftrightarrow &{\\begin{array}{*{20}{l}}
\n{{x^2} – {y^2} = 0}& \\wedge &{xy = 1}
\n\\end{array}} \\\\
\n{}& \\Leftrightarrow &{\\begin{array}{*{20}{l}}
\n{\\left( {y = x \\vee y =\u00a0 – x} \\right)}& \\wedge &{y = \\frac{1}{x}}
\n\\end{array}} \\\\
\n{}& \\Leftrightarrow &{\\begin{array}{*{20}{l}}
\n{\\left\\{ {\\begin{array}{*{20}{l}}
\n{x =\u00a0 – 1} \\\\
\n{y =\u00a0 – 1}
\n\\end{array}} \\right.}& \\vee &{\\left\\{ {\\begin{array}{*{20}{l}}
\n{x = 1} \\\\
\n{y = 1}
\n\\end{array}} \\right.}
\n\\end{array}}
\n\\end{array}$$
\n\u00ad<\/li>\n<\/ol>\n