Question
Answer
$$2i^3-i^4+3i^2+3i=i-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2i^3-i^4+3i^2+3i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2i-1-3+3i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}i-4\end{aligned} $$ | |
| ① | $$ 2i^3 = 2 \cdot \color{blue}{i^2} \cdot i =
2 \cdot ( \color{blue}{-1}) \cdot i =
-2 \cdot \, i $$ |
| ② | $$ -i^4 = - i^2 \cdot i^2 =
- ( - 1) \cdot ( - 1) =
-1 $$ |
| ③ | $$ 3i^2 = 3 \cdot (-1) = -3 $$ |
| ④ | Combine like terms: $$ \color{blue}{-2i} + \color{blue}{3i} \color{red}{-3} \color{red}{-1} = \color{blue}{i} \color{red}{-4} $$ |
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