Question
Answer
$$2\cdot\dfrac{a}{1+a-bi}=\dfrac{2a}{-bi+a+1}$$
Explanation
| $$ \begin{aligned}2 \cdot \frac{a}{1+a-bi}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2a}{-bi+a+1}\end{aligned} $$ | |
| ① | Multiply $2$ by $ \dfrac{a}{1+a-bi} $ to get $ \dfrac{2a}{-bi+a+1} $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{a}{1+a-bi} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{a}{1+a-bi} \xlongequal{\text{Step 2}} \frac{ 2 \cdot a }{ 1 \cdot \left( 1+a-bi \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a }{ 1+a-bi } = \frac{2a}{-bi+a+1} \end{aligned} $$ |
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