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Question

Answer

$$\dfrac{2}{8}-3i=\dfrac{-12i+1}{4}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{2}{8}-3i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ 2 : \color{orangered}{ 2 } }{ 8 : \color{orangered}{ 2 }} - 3i \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{4}-3i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-12i+1}{4}\end{aligned} $$
①
Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.
②

Subtract $3i$ from $ \dfrac{1}{4} $ to get $ \dfrac{ \color{purple}{ -12i+1 } }{ 4 }$.

Step 1: Write $ 3i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{4}$.

$$ \begin{aligned} \frac{1}{4} -3i & \xlongequal{\text{Step 1}} \frac{1}{4} - \frac{3i}{\color{red}{1}} = \frac{ 1 }{ 4 } - \frac{ 3i \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1 } }{ 4 } - \frac{ \color{purple}{ 12i } }{ 4 }=\frac{ \color{purple}{ -12i+1 } }{ 4 } \end{aligned} $$
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