\n$$\\left| {z – i} \\right| = \\left| {z – \\left( { – 1 – i} \\right)} \\right|$$<\/p>\n<\/blockquote>\n
Considerando $z = x + yi$, vem:<\/p>\n
$$\\begin{array}{*{20}{l}}
\n{\\left| {\\left( {x + yi} \\right) – i} \\right| = \\left| {\\left( {x + yi} \\right) – \\left( { – 1 – i} \\right)} \\right|}& \\Leftrightarrow &{\\left| {x + \\left( {y – 1} \\right)i} \\right| = \\left| {\\left( {x + 1} \\right) + \\left( {y + 1} \\right)i} \\right|} \\\\
\n{}& \\Leftrightarrow &{\\sqrt {{x^2} + {{\\left( {y – 1} \\right)}^2}}\u00a0 = \\sqrt {{{\\left( {x + 1} \\right)}^2} + {{\\left( {y + 1} \\right)}^2}} } \\\\
\n{}& \\Leftrightarrow &{{x^2} + {y^2} – 2y + 1 = {x^2} + 2x + 1 + {y^2} + 2y + 1} \\\\
\n{}& \\Leftrightarrow &{2x + 4y + 1 = 0} \\\\
\n{}& \\Leftrightarrow &{y =\u00a0 – \\frac{1}{2}x – \\frac{1}{4}}
\n\\end{array}$$<\/p>\n
A condi\u00e7\u00e3o define a mediatriz do segmento de reta [AB], sendo A o afixo do n\u00famero complexo ${z_1} = i$ e B o afixo de n\u00famero complexo ${z_2} =\u00a0 – 1 – i$.
\n\u00ad<\/p>\n