Answer
$$abs\frac{2+11i}{3-i}=\frac{7abis-abs}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}abs\frac{2+11i}{3-i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}abs\frac{-1+7i}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7abis-abs}{2}\end{aligned} $$ | |
| ① | Divide $ \, 2+11i \, $ by $ \, 3-i \, $ to get $\,\, \dfrac{-1+7i}{2} $. ( view steps ) |
| ② | Multiply $abs$ by $ \dfrac{-1+7i}{2} $ to get $ \dfrac{7abis-abs}{2} $. Step 1: Write $ abs $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} abs \cdot \frac{-1+7i}{2} & \xlongequal{\text{Step 1}} \frac{abs}{\color{red}{1}} \cdot \frac{-1+7i}{2} \xlongequal{\text{Step 2}} \frac{ abs \cdot \left( -1+7i \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -abs+7abis }{ 2 } = \frac{7abis-abs}{2} \end{aligned} $$ |
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