Multiply $qrst$ by $ \dfrac{1+i}{2} $ to get $ \dfrac{iqrst+qrst}{2} $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Add $ \dfrac{1}{2} $ and $ \dfrac{iqrst+qrst}{2} $ to get $ \dfrac{iqrst+qrst+1}{2} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{1}{2} + \frac{iqrst+qrst}{2} & = \frac{1}{\color{blue}{2}} + \frac{iqrst+qrst}{\color{blue}{2}} =\frac{ 1 + \left( iqrst+qrst \right) }{ \color{blue}{ 2 }} = \\[1ex] &= \frac{iqrst+qrst+1}{2} \end{aligned} $$