Question
Answer
$$2\cdot(3+4i)+i\cdot(5-6i)=13i+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\cdot(3+4i)+i\cdot(5-6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6+8i+5i-6i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6+8i+5i+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}13i+12\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 3+4i\right) $ $$ \color{blue}{2} \cdot \left( 3+4i\right) = 6+8i $$Multiply $ \color{blue}{i} $ by $ \left( 5-6i\right) $ $$ \color{blue}{i} \cdot \left( 5-6i\right) = 5i-6i^2 $$ |
| ② | $$ -6i^2 = -6 \cdot (-1) = 6 $$ |
| ③ | Combine like terms: $$ \color{blue}{6} + \color{red}{8i} + \color{red}{5i} + \color{blue}{6} = \color{red}{13i} + \color{blue}{12} $$ |
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