Question
Answer
$$(a-4i)\cdot(-6+4i)=4ai-6a+24i+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a-4i)\cdot(-6+4i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-6a+4ai+24i-16i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-6a+4ai+24i-(-16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4ai-6a+24i+16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a-4i}\right) $ by each term in $ \left( -6+4i\right) $. $$ \left( \color{blue}{a-4i}\right) \cdot \left( -6+4i\right) = -6a+4ai+24i-16i^2 $$ |
| ② | $$ 16i^2 = 16 \cdot (-1) = -16 $$ |
| ③ | Combine like terms: $$ 4ai-6a+24i+16 = 4ai-6a+24i+16 $$ |
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