Question
Answer
$$\dfrac{6+8i}{9}i=\dfrac{-8+6i}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6+8i}{9}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8i^2+6i}{9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-8+6i}{9}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{6+8i}{9} $ by $ i $ to get $ \dfrac{8i^2+6i}{9} $. 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. $$ \begin{aligned} \frac{6+8i}{9} \cdot i & \xlongequal{\text{Step 1}} \frac{6+8i}{9} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 6+8i \right) \cdot i }{ 9 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6i+8i^2 }{ 9 } = \frac{8i^2+6i}{9} \end{aligned} $$ |
| ② | $$ 8i^2 = 8 \cdot (-1) = -8 $$ |
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