Question
Answer
$$i^{10}+5i^8=-1+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{10}+5i^8& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-1+5\end{aligned} $$ | |
| ① | $$ i^{10} = i^{4 \cdot 2 + 2} =
\left( i^4 \right)^{ 2 } \cdot i^2 =
1^{ 2 } \cdot (-1) =
-1 = -1 $$ |
| ② | $$ 5i^8 = 5 \cdot i^{4 \cdot 2 + 0} =
5 \cdot \left( i^4 \right)^{ 2 } \cdot i^0 =
5 \cdot 1^{ 2 } \cdot 1 =
5 \cdot 1 $$ |
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