Question
Answer
$$5\cdot\dfrac{2-2i}{5+2-2i}=\dfrac{-50i+90}{53}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5 \cdot \frac{2-2i}{5+2-2i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5 \cdot \frac{2-2i}{-2i+7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5 \cdot \frac{18-10i}{53} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-50i+90}{53}\end{aligned} $$ | |
| ① | Simplify denominator $$ \color{blue}{5} + \color{blue}{2} -2i = -2i+ \color{blue}{7} $$ |
| ② | Divide $ \, 2-2i \, $ by $ \, 7-2i \, $ to get $\,\, \dfrac{18-10i}{53} $. ( view steps ) |
| ③ | Multiply $5$ by $ \dfrac{18-10i}{53} $ to get $ \dfrac{-50i+90}{53} $. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 5 \cdot \frac{18-10i}{53} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{18-10i}{53} \xlongequal{\text{Step 2}} \frac{ 5 \cdot \left( 18-10i \right) }{ 1 \cdot 53 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 90-50i }{ 53 } = \frac{-50i+90}{53} \end{aligned} $$ |
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