Answer
$$5-(-7+4i)-(-3-i)=-3i+15$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5-(-7+4i)-(-3-i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5+7-4i-(-3-i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4i+12-(-3-i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-4i+12+3+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-3i+15\end{aligned} $$ | |
| ① | Remove the parentheses by changing the sign of each term within them. $$ - \left( -7+4i \right) = 7-4i $$ |
| ② | Combine like terms: $$ \color{blue}{5} + \color{blue}{7} -4i = -4i+ \color{blue}{12} $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -3-i \right) = 3+i $$ |
| ④ | Combine like terms: $$ \color{blue}{-4i} + \color{red}{12} + \color{red}{3} + \color{blue}{i} = \color{blue}{-3i} + \color{red}{15} $$ |
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