Answer
$$(4-5i)\cdot(4+i)=-5i^2-16i+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-5i)\cdot(4+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16+4i-20i-5i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-5i^2-16i+16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4-5i}\right) $ by each term in $ \left( 4+i\right) $. $$ \left( \color{blue}{4-5i}\right) \cdot \left( 4+i\right) = 16+4i-20i-5i^2 $$ |
| ② | Combine like terms: $$ 16+ \color{blue}{4i} \color{blue}{-20i} -5i^2 = -5i^2 \color{blue}{-16i} +16 $$ |
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