Question
Answer
$$(i\cdot3185+4.611)\dfrac{3.3cos\cdot314t+1.25}{-i\cdot2414+i\cdot3185+4.611}=\dfrac{3000270ciost+3768cost+3185i+4}{771i+4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(i\cdot3185+4.611)\frac{3.3cos\cdot314t+1.25}{-i\cdot2414+i\cdot3185+4.611}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(i\cdot3185+4.611)\frac{3cos\cdot314t+1.25}{771i+4.611} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(i\cdot3185+4.611)\frac{942cost+1.25}{771i+4.611} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3000270ciost+3768cost+3185i+4}{771i+4}\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{-2414i} + \color{blue}{3185i} = \color{blue}{771i} $$ |
| ② | Combine like terms: $$ \color{blue}{-2414i} + \color{blue}{3185i} = \color{blue}{771i} $$ |
| ③ | Multiply $3185i+4$ by $ \dfrac{942cost+1}{771i+4} $ to get $ \dfrac{3000270ciost+3768cost+3185i+4}{771i+4} $. Step 1: Write $ 3185i+4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3185i+4 \cdot \frac{942cost+1}{771i+4} & \xlongequal{\text{Step 1}} \frac{3185i+4}{\color{red}{1}} \cdot \frac{942cost+1}{771i+4} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 3185i+4 \right) \cdot \left( 942cost+1 \right) }{ 1 \cdot \left( 771i+4 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3000270ciost+3185i+3768cost+4 }{ 771i+4 } = \frac{3000270ciost+3768cost+3185i+4}{771i+4} \end{aligned} $$ |
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