Answer
$$z\frac{i}{y}i=\frac{i^2z}{y}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}z\frac{i}{y}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{iz}{y}i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{i^2z}{y}\end{aligned} $$ | |
| ① | Multiply $z$ by $ \dfrac{i}{y} $ to get $ \dfrac{ iz }{ y } $. Step 1: Write $ z $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} z \cdot \frac{i}{y} & \xlongequal{\text{Step 1}} \frac{z}{\color{red}{1}} \cdot \frac{i}{y} \xlongequal{\text{Step 2}} \frac{ z \cdot i }{ 1 \cdot y } \xlongequal{\text{Step 3}} \frac{ iz }{ y } \end{aligned} $$ |
| ② | Multiply $ \dfrac{iz}{y} $ by $ i $ to get $ \dfrac{ i^2z }{ y } $. 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. $$ \begin{aligned} \frac{iz}{y} \cdot i & \xlongequal{\text{Step 1}} \frac{iz}{y} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ iz \cdot i }{ y \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ i^2z }{ y } \end{aligned} $$ |
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