Answer
$$6(5-5i)^2-11\cdot(5-5i)+4+5i=-240i-51$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6(5-5i)^2-11\cdot(5-5i)+4+5i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6(25-50i+25i^2)-11\cdot(5-5i)+4+5i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6(25-50i-25)-11\cdot(5-5i)+4+5i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6\cdot-50i-11\cdot(5-5i)+4+5i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-300i-(55-55i)+4+5i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-300i-55+55i+4+5i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-240i-51\end{aligned} $$ | |
| ① | Find $ \left(5-5i\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5 } $ and $ B = \color{red}{ 5i }$. $$ \begin{aligned}\left(5-5i\right)^2 = \color{blue}{5^2} -2 \cdot 5 \cdot 5i + \color{red}{\left( 5i \right)^2} = 25-50i+25i^2\end{aligned} $$ |
| ② | $$ 25i^2 = 25 \cdot (-1) = -25 $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ \cancel{25}} \,-50i \, \color{blue}{ -\cancel{25}} \, = -50i $$ |
| ④ | Multiply $ \color{blue}{11} $ by $ \left( 5-5i\right) $ $$ \color{blue}{11} \cdot \left( 5-5i\right) = 55-55i $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 55-55i \right) = -55+55i $$ |
| ⑥ | Combine like terms: $$ \color{blue}{-300i} \color{red}{-55} + \color{green}{55i} + \color{red}{4} + \color{green}{5i} = \color{green}{-240i} \color{red}{-51} $$ |
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