Question
Answer
$$3(2-5i)^2=-60i-63$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(2-5i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(4-20i+25i^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3(4-20i-25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3(-20i-21) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-60i-63\end{aligned} $$ | |
| ① | Find $ \left(2-5i\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2 } $ and $ B = \color{red}{ 5i }$. $$ \begin{aligned}\left(2-5i\right)^2 = \color{blue}{2^2} -2 \cdot 2 \cdot 5i + \color{red}{\left( 5i \right)^2} = 4-20i+25i^2\end{aligned} $$ |
| ② | $$ 25i^2 = 25 \cdot (-1) = -25 $$ |
| ③ | Combine like terms: $$ \color{blue}{4} -20i \color{blue}{-25} = -20i \color{blue}{-21} $$ |
| ④ | Multiply $ \color{blue}{3} $ by $ \left( -20i-21\right) $ $$ \color{blue}{3} \cdot \left( -20i-21\right) = -60i-63 $$ |
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