Question
Answer
$$4\cdot(2+3i)-5\cdot(1-2i)=22i+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\cdot(2+3i)-5\cdot(1-2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8+12i-(5-10i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8+12i-5+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}22i+3\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( 2+3i\right) $ $$ \color{blue}{4} \cdot \left( 2+3i\right) = 8+12i $$Multiply $ \color{blue}{5} $ by $ \left( 1-2i\right) $ $$ \color{blue}{5} \cdot \left( 1-2i\right) = 5-10i $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5-10i \right) = -5+10i $$ |
| ③ | Combine like terms: $$ \color{blue}{8} + \color{red}{12i} \color{blue}{-5} + \color{red}{10i} = \color{red}{22i} + \color{blue}{3} $$ |
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