Gọi \(z_1\) và \(z_2\)

A

- Hướng dẫn giải

\({z^2} - 2z + 5 = 0 \Rightarrow \left\{ \begin{array}{l} z = 1 - 2i\\ z = 1 + 2i \end{array} \right.\)

\(\begin{array}{*{20}{l}}
\begin{array}{l}
 \Rightarrow P = {z_1}^4 + {z_2}^4\\
 = {\left( {{z_1}^2 + {z_2}^2} \right)^2} + 2{z_1}^2.{z_2}^2
\end{array}\\
\begin{array}{l}
 = {\left( {{{\left( {1 - 2i} \right)}^2} + {{\left( {1 + 2i} \right)}^2}} \right)^2}\\
\,\, - 2{\left( {(1 - 2i)(1 + 2i)} \right)^2}\\
 = 36 - 50 =  - 14.
\end{array}
\end{array}\)