Đặt \(z = x + yi\,(x,y \in R)\)
\(z + z.\overline z = \frac{i}{2} \Leftrightarrow x + iy + {x^2} + {y^2} = \frac{i}{2}\)
\(\Leftrightarrow \left\{ \begin{array}{l} x + {x^2} + {y^2} = 0\\ y = \frac{1}{2} \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x = - \frac{1}{2}\\ y =...