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Question

Answer

$$5000\cdot\dfrac{\dfrac{6}{10}i+0.02}{3\cdot(2+\dfrac{6}{10}i)(20+\dfrac{6}{10}i)^2}=5000\cdot\dfrac{\dfrac{3i}{5}}{\dfrac{9i+30}{5}(20+\dfrac{6}{10}i)^2}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}5000 \cdot \frac{\frac{6}{10}i+0.02}{3\cdot(2+\frac{6}{10}i)(20+\frac{6}{10}i)^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5000 \cdot \left(\frac{ \frac{ 6 : \color{orangered}{ 2 } }{ 10 : \color{orangered}{ 2 }} \cdot i + 0.02 }{ \left(3 \cdot \left(2 + \frac{ 6 : \color{orangered}{ 2 } }{ 10 : \color{orangered}{ 2 }} \cdot i\right)\right) \cdot \left((20+\frac{6}{10}i)^2\right) }\right) \xlongequal{ } \\[1 em] & \xlongequal{ }5000 \cdot \frac{\frac{3}{5}i+0.02}{3\cdot(2+\frac{3}{5}i)(20+\frac{6}{10}i)^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5000 \cdot \frac{\frac{3i}{5}+0.02}{3\cdot(2+\frac{3i}{5})(20+\frac{6}{10}i)^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}5000 \cdot \frac{\frac{3i}{5}}{3\frac{3i+10}{5}(20+\frac{6}{10}i)^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}5000 \cdot \frac{\frac{3i}{5}}{\frac{9i+30}{5}(20+\frac{6}{10}i)^2}\end{aligned} $$
①
Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.
②
Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.
③

Multiply $ \dfrac{3}{5} $ by $ i $ to get $ \dfrac{ 3i }{ 5 } $.

Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{5} \cdot i & \xlongequal{\text{Step 1}} \frac{3}{5} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot i }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3i }{ 5 } \end{aligned} $$
④

Multiply $ \dfrac{3}{5} $ by $ i $ to get $ \dfrac{ 3i }{ 5 } $.

Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{5} \cdot i & \xlongequal{\text{Step 1}} \frac{3}{5} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot i }{ 5 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3i }{ 5 } \end{aligned} $$
⑤

Add $ \dfrac{3i}{5} $ and $ 0 $ to get $ \dfrac{ \color{purple}{ 3i } }{ 5 }$.

Step 1: Write $ 0 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{3i}{5} +0 & \xlongequal{\text{Step 1}} \frac{3i}{5} + \frac{0}{\color{red}{1}} = \frac{ 3i }{ 5 } + \frac{ 0 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3i } }{ 5 } + \frac{ \color{purple}{ 0 } }{ 5 }=\frac{ \color{purple}{ 3i } }{ 5 } \end{aligned} $$
⑥

Add $2$ and $ \dfrac{3i}{5} $ to get $ \dfrac{ \color{purple}{ 3i+10 } }{ 5 }$.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 5 }$.

$$ \begin{aligned} 2+ \frac{3i}{5} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} + \frac{3i}{5} = \frac{ 2 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} + \frac{ 3i }{ 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10 } }{ 5 } + \frac{ \color{purple}{ 3i } }{ 5 }=\frac{ \color{purple}{ 3i+10 } }{ 5 } \end{aligned} $$
⑦

Add $ \dfrac{3i}{5} $ and $ 0 $ to get $ \dfrac{ \color{purple}{ 3i } }{ 5 }$.

Step 1: Write $ 0 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{3i}{5} +0 & \xlongequal{\text{Step 1}} \frac{3i}{5} + \frac{0}{\color{red}{1}} = \frac{ 3i }{ 5 } + \frac{ 0 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3i } }{ 5 } + \frac{ \color{purple}{ 0 } }{ 5 }=\frac{ \color{purple}{ 3i } }{ 5 } \end{aligned} $$
⑧

Multiply $3$ by $ \dfrac{3i+10}{5} $ to get $ \dfrac{ 9i+30 }{ 5 } $.

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.

$$ \begin{aligned} 3 \cdot \frac{3i+10}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{3i+10}{5} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( 3i+10 \right) }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9i+30 }{ 5 } \end{aligned} $$
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