Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 617

\[1)\ z + 3\overline{z} = 8 + 12i\]

\[z = x + yi:\]

\[(x + yi) + 3(x - yi) = 8 + 12i\]

\[x + yi + 3x - 3yi = 8 + 12i\]

\[4x - 2yi = 8 + 12i\]

\[4x = 8\]

\[x = 2.\]

\[- 2y = 12\]

\[y = - 6.\]

\[Ответ:\ \ z = 2 - 6i.\]

\[2)\ 4z - \overline{z} = - 9 + 10i\]

\[z = x + yi:\]

\[4(x + yi) - (x - yi) = - 9 + 10i\]

\[4x + 4yi - x + yi = - 9 + 10i\]

\[3x + 5yi = - 9 + 10i\]

\[3x = - 9\]

\[x = - 3.\]

\[5y = 10\]

\[y = 2.\]

\[Ответ:\ \ z = - 3 + 2i.\]