Answer
$$\frac{5+3i}{i\cdot(2+6i)}=\frac{-6-7i}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5+3i}{i\cdot(2+6i)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5+3i}{2i+6i^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5+3i}{2i-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-6-7i}{10}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{i} $ by $ \left( 2+6i\right) $ $$ \color{blue}{i} \cdot \left( 2+6i\right) = 2i+6i^2 $$ |
| ② | $$ 6i^2 = 6 \cdot (-1) = -6 $$ |
| ③ | Divide $ \, 5+3i \, $ by $ \, -6+2i \, $ to get $\,\, \dfrac{-6-7i}{10} $. ( view steps ) |
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