Question
Answer
$$\dfrac{6-5i}{3}i=\dfrac{5+6i}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6-5i}{3}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-5i^2+6i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5+6i}{3}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{6-5i}{3} $ by $ i $ to get $ \dfrac{-5i^2+6i}{3} $. 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. $$ \begin{aligned} \frac{6-5i}{3} \cdot i & \xlongequal{\text{Step 1}} \frac{6-5i}{3} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 6-5i \right) \cdot i }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6i-5i^2 }{ 3 } = \frac{-5i^2+6i}{3} \end{aligned} $$ |
| ② | $$ -5i^2 = -5 \cdot (-1) = 5 $$ |
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