Question
Answer
$$\dfrac{4+5i}{4}i=\dfrac{-5+4i}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4+5i}{4}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5i^2+4i}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-5+4i}{4}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{4+5i}{4} $ by $ i $ to get $ \dfrac{5i^2+4i}{4} $. 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. $$ \begin{aligned} \frac{4+5i}{4} \cdot i & \xlongequal{\text{Step 1}} \frac{4+5i}{4} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 4+5i \right) \cdot i }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4i+5i^2 }{ 4 } = \frac{5i^2+4i}{4} \end{aligned} $$ |
| ② | $$ 5i^2 = 5 \cdot (-1) = -5 $$ |
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