Answer
$$7\cdot(3-5i)+(4-2i)\cdot(-6+7i)=5i+11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7\cdot(3-5i)+(4-2i)\cdot(-6+7i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}21-35i-24+28i+12i-14i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}21-35i-14i^2+40i-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}21-35i+14+40i-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}21-35i+40i-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}5i+11\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{7} $ by $ \left( 3-5i\right) $ $$ \color{blue}{7} \cdot \left( 3-5i\right) = 21-35i $$ Multiply each term of $ \left( \color{blue}{4-2i}\right) $ by each term in $ \left( -6+7i\right) $. $$ \left( \color{blue}{4-2i}\right) \cdot \left( -6+7i\right) = -24+28i+12i-14i^2 $$ |
| ② | Combine like terms: $$ -24+ \color{blue}{28i} + \color{blue}{12i} -14i^2 = -14i^2+ \color{blue}{40i} -24 $$ |
| ③ | $$ -14i^2 = -14 \cdot (-1) = 14 $$ |
| ④ | Combine like terms: $$ \color{blue}{14} +40i \color{blue}{-24} = 40i \color{blue}{-10} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{21} \color{red}{-35i} + \color{red}{40i} \color{blue}{-10} = \color{red}{5i} + \color{blue}{11} $$ |
This page was created using
Complex Expression calculator