Answer
$$z^2-(1+2i)z-(9+13i)=-2iz+z^2-13i-z-9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}z^2-(1+2i)z-(9+13i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}z^2-(1z+2iz)-(9+13i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}z^2-z-2iz-(9+13i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}z^2-z-2iz-9-13i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-2iz+z^2-13i-z-9\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{1+2i}\right) \cdot z = z+2iz $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( z+2iz \right) = -z-2iz $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9+13i \right) = -9-13i $$ |
| ④ | Combine like terms: $$ -2iz+z^2-13i-z-9 = -2iz+z^2-13i-z-9 $$ |
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