Question
Answer
$$\dfrac{i}{5}i=-\dfrac{1}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{i}{5}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{i^2}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{1}{5}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{i}{5} $ by $ i $ to get $ \dfrac{ i^2 }{ 5 } $. 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. $$ \begin{aligned} \frac{i}{5} \cdot i & \xlongequal{\text{Step 1}} \frac{i}{5} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ i \cdot i }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ i^2 }{ 5 } \end{aligned} $$ |
| ② | $$ i^2 = -1 $$ |
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