Question
Answer
$$(-7i)\dfrac{3}{8}i=\dfrac{21}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-7i)\frac{3}{8}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-7i)\frac{3i}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{21i^2}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{21}{8}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{3}{8} $ by $ i $ to get $ \dfrac{ 3i }{ 8 } $. 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. $$ \begin{aligned} \frac{3}{8} \cdot i & \xlongequal{\text{Step 1}} \frac{3}{8} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot i }{ 8 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3i }{ 8 } \end{aligned} $$ |
| ② | Multiply $-7i$ by $ \dfrac{3i}{8} $ to get $ \dfrac{ -21i^2 }{ 8 } $. Step 1: Write $ -7i $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} -7i \cdot \frac{3i}{8} & \xlongequal{\text{Step 1}} \frac{-7i}{\color{red}{1}} \cdot \frac{3i}{8} \xlongequal{\text{Step 2}} \frac{ \left( -7i \right) \cdot 3i }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -21i^2 }{ 8 } \end{aligned} $$ |
| ③ | $$ -21i^2 = -21 \cdot (-1) = 21 $$ |
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