Divide $ \, i \, $ by $ \, 8+8i \, $ to get $\,\, \dfrac{1+i}{16} $.
( view steps )

Multiply $64$ by $ \dfrac{1+i}{16} $ to get $ \dfrac{64i+64}{16} $.

Step 1: Write $ 64 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 64 \cdot \frac{1+i}{16} & \xlongequal{\text{Step 1}} \frac{64}{\color{red}{1}} \cdot \frac{1+i}{16} \xlongequal{\text{Step 2}} \frac{ 64 \cdot \left( 1+i \right) }{ 1 \cdot 16 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 64+64i }{ 16 } = \frac{64i+64}{16} \end{aligned} $$

Add $4$ and $ \dfrac{64i+64}{16} $ to get $ \dfrac{ \color{purple}{ 64i+128 } }{ 16 }$.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 16 }$.

$$ \begin{aligned} 4+ \frac{64i+64}{16} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} + \frac{64i+64}{16} = \frac{ 4 \cdot \color{blue}{ 16 }}{ 1 \cdot \color{blue}{ 16 }} + \frac{ 64i+64 }{ 16 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 64 } }{ 16 } + \frac{ \color{purple}{ 64i+64 } }{ 16 }=\frac{ \color{purple}{ 64i+128 } }{ 16 } \end{aligned} $$