Cho số phức \(z = - \dfrac{1}{2} + \dfrac{{\sqrt 3 }}{2}i\). Khi đó số phức \({\left( {\overline z } \right)^2}\) bằng ;

* Hướng dẫn giải

\(\begin{array}{l}z =  - \dfrac{1}{2} + \dfrac{{\sqrt 3 }}{2}i\\ \Rightarrow {\left( {\overline z } \right)^2} = {\left( { - \dfrac{1}{2} - \dfrac{{\sqrt 3 }}{2}i} \right)^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{{{\left( {1 + \sqrt 3 i} \right)}^2}}}{4}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{ - 2 + 2\sqrt 3 i}}{4}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, =  - \dfrac{1}{2} + \dfrac{{\sqrt 3 }}{2}i\end{array}\)