Question
Answer
$$(48-14i)(a+8i)=-14ai+48a+384i+112$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(48-14i)(a+8i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}48a+384i-14ai-112i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}48a+384i-14ai-(-112) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-14ai+48a+384i+112\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{48-14i}\right) $ by each term in $ \left( a+8i\right) $. $$ \left( \color{blue}{48-14i}\right) \cdot \left( a+8i\right) = 48a+384i-14ai-112i^2 $$ |
| ② | $$ 112i^2 = 112 \cdot (-1) = -112 $$ |
| ③ | Combine like terms: $$ -14ai+48a+384i+112 = -14ai+48a+384i+112 $$ |
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