Cho số phức z=a+bi (a,b thuộc R) thỏa mãn

Đáp án D

Giả sử \(z = a + bi\left( {a,b \in R} \right)\)

Ta có \(\left\{ {\begin{array}{*{20}{l}}{\left| {z - 2} \right| = \left| z \right|}\\{\left( {z + 1} \right)\left( {\bar z - i} \right) \in R}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{\left| {a - 2 + bi} \right| = \left| {a + bi} \right|}\\{\left( {a + 1 + bi} \right)\left[ {a - \left( {b + 1} \right)i} \right] \in R}\end{array}} \right.\)

\( \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{{\left( {a - 2} \right)}^2} + {b^2} = {a^2} + {b^2}}\\{a\left( {a + 1} \right) + b\left( {b + 1} \right) - \left( {a + b + 1} \right)i \in }\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{a = 1}\\{a + b + 1 = 0}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{a = 1}\\{b = - 2}\end{array}} \right. \Rightarrow a + b = - 1.\)