$$\dfrac{1}{s}qrt\cdot(1+2i)=\dfrac{2iqrt+qrt}{s}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{s}qrt\cdot(1+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{q}{s}rt\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{qr}{s}t\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{qrt}{s}\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{2iqrt+qrt}{s}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{s} $ by $ q $ to get $ \dfrac{ q }{ s } $. Step 1: Write $ q $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{1}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot q }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ q }{ s } \end{aligned} $$ |
| ② | Multiply $ \dfrac{q}{s} $ by $ r $ to get $ \dfrac{ qr }{ s } $. Step 1: Write $ r $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{q}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{q}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ q \cdot r }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ qr }{ s } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{qr}{s} $ by $ t $ to get $ \dfrac{ qrt }{ s } $. Step 1: Write $ t $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{qr}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{qr}{s} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ qr \cdot t }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ qrt }{ s } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{qrt}{s} $ by $ 1+2i $ to get $ \dfrac{2iqrt+qrt}{s} $. Step 1: Write $ 1+2i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{qrt}{s} \cdot 1+2i & \xlongequal{\text{Step 1}} \frac{qrt}{s} \cdot \frac{1+2i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ qrt \cdot \left( 1+2i \right) }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ qrt+2iqrt }{ s } = \frac{2iqrt+qrt}{s} \end{aligned} $$ |