Question
Answer
$$4-3\cdot\dfrac{i}{3}i=4+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4-3 \cdot \frac{i}{3}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4-ii \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4-i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4+1\end{aligned} $$ | |
| ① | Multiply $3$ by $ \dfrac{i}{3} $ to get $ i$. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Cancel $ \color{blue}{ 3 } $ in first and second fraction. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} 3 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{i}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 \cdot i }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ i }{ 1 } =i \end{aligned} $$ |
| ② | $$ 1 i i = i^{1 + 1} = i^2 $$ |
| ③ | $$ -i^2 = -(-1) = 1 $$ |
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