Answer
$$(4-6i)^2=-48i-20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-6i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16-48i+36i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16-48i-36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-48i-20\end{aligned} $$ | |
| ① | Find $ \left(4-6i\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4 } $ and $ B = \color{red}{ 6i }$. $$ \begin{aligned}\left(4-6i\right)^2 = \color{blue}{4^2} -2 \cdot 4 \cdot 6i + \color{red}{\left( 6i \right)^2} = 16-48i+36i^2\end{aligned} $$ |
| ② | $$ 36i^2 = 36 \cdot (-1) = -36 $$ |
| ③ | Combine like terms: $$ -48i+ \color{blue}{16} \color{blue}{-36} = -48i \color{blue}{-20} $$ |
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