Answer
$$3\cdot(1+2i)-(2-i)+2\cdot(4+5i)=17i+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\cdot(1+2i)-(2-i)+2\cdot(4+5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3+6i-(2-i)+8+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3+6i-2+i+8+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}7i+1+8+10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}17i+9\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 1+2i\right) $ $$ \color{blue}{3} \cdot \left( 1+2i\right) = 3+6i $$Multiply $ \color{blue}{2} $ by $ \left( 4+5i\right) $ $$ \color{blue}{2} \cdot \left( 4+5i\right) = 8+10i $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2-i \right) = -2+i $$ |
| ③ | Combine like terms: $$ \color{blue}{3} + \color{red}{6i} \color{blue}{-2} + \color{red}{i} = \color{red}{7i} + \color{blue}{1} $$ |
| ④ | Combine like terms: $$ \color{blue}{7i} + \color{red}{1} + \color{red}{8} + \color{blue}{10i} = \color{blue}{17i} + \color{red}{9} $$ |
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