Question
Answer
$$(3-2i)^2-(5i+7)=-17i-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3-2i)^2-(5i+7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9-12i+4i^2-(5i+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9-12i-4-(5i+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-12i+5-(5i+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-12i+5-5i-7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-17i-2\end{aligned} $$ | |
| ① | Find $ \left(3-2i\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3 } $ and $ B = \color{red}{ 2i }$. $$ \begin{aligned}\left(3-2i\right)^2 = \color{blue}{3^2} -2 \cdot 3 \cdot 2i + \color{red}{\left( 2i \right)^2} = 9-12i+4i^2\end{aligned} $$ |
| ② | $$ 4i^2 = 4 \cdot (-1) = -4 $$ |
| ③ | Combine like terms: $$ \color{blue}{9} -12i \color{blue}{-4} = -12i+ \color{blue}{5} $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5i+7 \right) = -5i-7 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-12i} + \color{red}{5} \color{blue}{-5i} \color{red}{-7} = \color{blue}{-17i} \color{red}{-2} $$ |
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