Question
Answer
$$7.07\cdot\dfrac{2+1.591i}{1.9+1.591i}=\dfrac{-7i+21}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7.07 \cdot \frac{2+1.591i}{1.9+1.591i}& \xlongequal{ }7.07 \cdot \frac{2+i}{1.9+i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7.07 \cdot \frac{3-i}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-7i+21}{2}\end{aligned} $$ | |
| ① | Divide $ \, 2+i \, $ by $ \, 1+i \, $ to get $\,\, \dfrac{3-i}{2} $. ( view steps ) |
| ② | Multiply $7$ by $ \dfrac{3-i}{2} $ to get $ \dfrac{-7i+21}{2} $. Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 7 \cdot \frac{3-i}{2} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{3-i}{2} \xlongequal{\text{Step 2}} \frac{ 7 \cdot \left( 3-i \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 21-7i }{ 2 } = \frac{-7i+21}{2} \end{aligned} $$ |
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