Question
Answer
$$3+4i+2i\cdot(2-5i)=8i+13$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3+4i+2i\cdot(2-5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3+4i+4i-10i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3+4i+4i+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8i+13\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2i} $ by $ \left( 2-5i\right) $ $$ \color{blue}{2i} \cdot \left( 2-5i\right) = 4i-10i^2 $$ |
| ② | $$ -10i^2 = -10 \cdot (-1) = 10 $$ |
| ③ | Combine like terms: $$ \color{blue}{3} + \color{red}{4i} + \color{red}{4i} + \color{blue}{10} = \color{red}{8i} + \color{blue}{13} $$ |
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