Multiply $ \dfrac{1}{600} $ by $ i $ to get $ \dfrac{ i }{ 600 } $.

Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{600} \cdot i & \xlongequal{\text{Step 1}} \frac{1}{600} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot i }{ 600 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ i }{ 600 } \end{aligned} $$

Add $ \dfrac{1}{3000} $ and $ \dfrac{i}{600} $ to get $ \dfrac{ \color{purple}{ 5i+1 } }{ 3000 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{1}{3000} + \frac{i}{600} & = \frac{ 1 }{ 3000 } + \frac{ i \cdot \color{blue}{ 5 }}{ 600 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 1 } }{ 3000 } + \frac{ \color{purple}{ 5i } }{ 3000 }=\frac{ \color{purple}{ 5i+1 } }{ 3000 } \end{aligned} $$

Divide $1$ by $ \dfrac{5i+1}{3000} $ to get $ \dfrac{ 3000 }{ 5i+1 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ 1 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{ \frac{\color{blue}{5i+1}}{\color{blue}{3000}} } & \xlongequal{\text{Step 1}} 1 \cdot \frac{\color{blue}{3000}}{\color{blue}{5i+1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{1}{\color{red}{1}} \cdot \frac{3000}{5i+1} \xlongequal{\text{Step 3}} \frac{ 1 \cdot 3000 }{ 1 \cdot \left( 5i+1 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 3000 }{ 5i+1 } \end{aligned} $$