Question
Answer
$$i^3+2i^5-3i^4-4i^{10}=-i+2i-3+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^3+2i^5-3i^4-4i^{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-i+2i-3+4\end{aligned} $$ | |
| ① | $$ i^3 = \color{blue}{i^2} \cdot i =
( \color{blue}{-1}) \cdot i =
- \, i $$ |
| ② | $$ 2i^5 = 2 \cdot i^{4 \cdot 1 + 1} =
2 \cdot \left( i^4 \right)^{ 1 } \cdot i^1 =
2 \cdot 1^{ 1 } \cdot i =
2 \cdot i $$ |
| ③ | $$ -3i^4 = -3 \cdot i^2 \cdot i^2 =
-3 \cdot ( - 1) \cdot ( - 1) =
-3 $$ |
| ④ | $$ -4i^{10} = -4 \cdot i^{4 \cdot 2 + 2} =
-4 \cdot \left( i^4 \right)^{ 2 } \cdot i^2 =
-4 \cdot 1^{ 2 } \cdot (-1) =
-4 \cdot -1 = 4 $$ |
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