Answer
$$(-2+3i)^2=-12i-5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-2+3i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4-12i+9i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4-12i-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-12i-5\end{aligned} $$ | |
| ① | Find $ \left(-2+3i\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply 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 }$. $$ \begin{aligned}\left(-2+3i\right)^2& \xlongequal{ S1 } \left(2-3i\right)^2 \xlongequal{ S2 } \color{blue}{2^2} -2 \cdot 2 \cdot 3i + \color{red}{\left( 3i \right)^2} = \\[1 em] & = 4-12i+9i^2\end{aligned} $$ |
| ② | $$ 9i^2 = 9 \cdot (-1) = -9 $$ |
| ③ | Combine like terms: $$ -12i+ \color{blue}{4} \color{blue}{-9} = -12i \color{blue}{-5} $$ |
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