Question
Answer
$$z^2+(2+3i)z-(4.25+i)=3iz+z^2-i+2z-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}z^2+(2+3i)z-(4.25+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}z^2+2z+3iz-(4.25+i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3iz+z^2+2z-(4.25+i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3iz+z^2+2z-4-i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3iz+z^2-i+2z-4\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{2+3i}\right) \cdot z = 2z+3iz $$ |
| ② | Combine like terms: $$ z^2+2z+3iz = 3iz+z^2+2z $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4+i \right) = -4-i $$ |
| ④ | Combine like terms: $$ 3iz+z^2-i+2z-4 = 3iz+z^2-i+2z-4 $$ |
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