ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 656

\[1)\ z^{2} + (2 - 6i)z - 12 - 6i = 0\]

\[D = (2 - 6i)^{2} + 4(12 + 6i) =\]

\[= 4 - 24i - 36 + 48 + 24i = 16\]

\[z_{1} = \frac{- (2 - 6i) - 4}{2} = \frac{- 6 + 6i}{2} =\]

\[= - 3 + 3i;\]

\[z_{2} = \frac{- (2 - 6i) + 4}{2} = \frac{2 + 6i}{2} =\]

\[= 1 + 3i.\]

\[Ответ:\ - 3 + 3i;\ 1 + 3i.\]

\[2)\ z^{2} - 2(1 + i)z + 9 + 2i = 0\]

\[D = 4(1 + i)^{2} - 4(9 + 2i) =\]

\[= 4(1 + 2i - 1 - 9 - 2i) = - 36\]

\[z_{1} = \frac{2(1 + i) - 6i}{2} = \frac{2 - 4i}{2} =\]

\[= 1 - 2i;\]

\[z_{2} = \frac{2(1 + i) + 6i}{2} = \frac{2 + 8i}{2} =\]

\[= 1 + 4i.\]

\[Ответ:\ \ 1 - 2i;\ 1 + 4i.\]