Question
Answer
$$3\cdot(5-2i)-4(2-3i)^2=42i+35$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\cdot(5-2i)-4(2-3i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3\cdot(5-2i)-4(4-12i+9i^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot(5-2i)-4(4-12i-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\cdot(5-2i)-4(-12i-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}15-6i-(-48i-20) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}15-6i+48i+20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}42i+35\end{aligned} $$ | |
| ① | Find $ \left(2-3i\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2 } $ and $ B = \color{red}{ 3i }$. $$ \begin{aligned}\left(2-3i\right)^2 = \color{blue}{2^2} -2 \cdot 2 \cdot 3i + \color{red}{\left( 3i \right)^2} = 4-12i+9i^2\end{aligned} $$ |
| ② | $$ 9i^2 = 9 \cdot (-1) = -9 $$ |
| ③ | Combine like terms: $$ \color{blue}{4} -12i \color{blue}{-9} = -12i \color{blue}{-5} $$ |
| ④ | Multiply $ \color{blue}{3} $ by $ \left( 5-2i\right) $ $$ \color{blue}{3} \cdot \left( 5-2i\right) = 15-6i $$Multiply $ \color{blue}{4} $ by $ \left( -12i-5\right) $ $$ \color{blue}{4} \cdot \left( -12i-5\right) = -48i-20 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -48i-20 \right) = 48i+20 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{15} \color{red}{-6i} + \color{red}{48i} + \color{blue}{20} = \color{red}{42i} + \color{blue}{35} $$ |
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