Question
Answer
$$\dfrac{1}{1+3i}\cdot\dfrac{1}{3}=\dfrac{1}{9i+3}$$
Explanation
| $$ \begin{aligned}\frac{1}{1+3i}\cdot\frac{1}{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{9i+3}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{1+3i} $ by $ \dfrac{1}{3} $ to get $ \dfrac{1}{9i+3} $. Step 1: Multiply numerators and denominators. Step 2: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{1+3i} \cdot \frac{1}{3} & \xlongequal{\text{Step 1}} \frac{ 1 \cdot 1 }{ \left( 1+3i \right) \cdot 3 } \xlongequal{\text{Step 2}} \frac{ 1 }{ 3+9i } = \\[1ex] &= \frac{1}{9i+3} \end{aligned} $$ |
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