Answer
$$\frac{10+5i-8i-4i^2}{3-3i+2i-2i^2}=\frac{73-i}{26}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10+5i-8i-4i^2}{3-3i+2i-2i^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10+5i-8i+4}{3-3i+2i-2i^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10+5i-8i+4}{3-3i+2i+2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-3i+14}{3-3i+2i+2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-3i+14}{-i+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{73-i}{26}\end{aligned} $$ | |
| ① | $$ -4i^2 = -4 \cdot (-1) = 4 $$ |
| ② | $$ -2i^2 = -2 \cdot (-1) = 2 $$ |
| ③ | Simplify numerator $$ \color{blue}{10} + \color{red}{5i} \color{red}{-8i} + \color{blue}{4} = \color{red}{-3i} + \color{blue}{14} $$ |
| ④ | Simplify denominator $$ \color{blue}{3} \color{red}{-3i} + \color{red}{2i} + \color{blue}{2} = \color{red}{-i} + \color{blue}{5} $$ |
| ⑤ | Divide $ \, 14-3i \, $ by $ \, 5-i \, $ to get $\,\, \dfrac{73-i}{26} $. ( view steps ) |
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