Question
Answer
$$3\cdot\dfrac{40-i\cdot70+i\cdot50}{50+3\cdot(40-i\cdot70)}=\dfrac{15i+33}{73}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{40-i\cdot70+i\cdot50}{50+3\cdot(40-i\cdot70)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3 \cdot \frac{40-i\cdot70+i\cdot50}{50+120-210i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3 \cdot \frac{-20i+40}{-210i+170} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3 \cdot \frac{11+5i}{73} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{15i+33}{73}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 40-70i\right) $ $$ \color{blue}{3} \cdot \left( 40-70i\right) = 120-210i $$ |
| ② | Combine like terms: $$ 40 \color{blue}{-70i} + \color{blue}{50i} = \color{blue}{-20i} +40 $$ |
| ③ | Combine like terms: $$ \color{blue}{50} + \color{blue}{120} -210i = -210i+ \color{blue}{170} $$ |
| ④ | Divide $ \, 40-20i \, $ by $ \, 170-210i \, $ to get $\,\, \dfrac{11+5i}{73} $. ( view steps ) |
| ⑤ | Multiply $3$ by $ \dfrac{11+5i}{73} $ to get $ \dfrac{15i+33}{73} $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3 \cdot \frac{11+5i}{73} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{11+5i}{73} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( 11+5i \right) }{ 1 \cdot 73 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 33+15i }{ 73 } = \frac{15i+33}{73} \end{aligned} $$ |
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