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