Question
Answer
$$2i\cdot(3-5i)-(-9+4i)=2i+19$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2i\cdot(3-5i)-(-9+4i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6i-10i^2-(-9+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6i+10-(-9+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6i+10+9-4i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2i+19\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2i} $ by $ \left( 3-5i\right) $ $$ \color{blue}{2i} \cdot \left( 3-5i\right) = 6i-10i^2 $$ |
| ② | $$ -10i^2 = -10 \cdot (-1) = 10 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -9+4i \right) = 9-4i $$ |
| ④ | Combine like terms: $$ \color{blue}{6i} + \color{red}{10} + \color{red}{9} \color{blue}{-4i} = \color{blue}{2i} + \color{red}{19} $$ |
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