Question
Answer
$$i^{35}+i^{20}=-i+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{35}+i^{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i+1\end{aligned} $$ | |
| ① | $$ i^{35} = i^{4 \cdot 8 + 3} =
\left( i^4 \right)^{ 8 } \cdot i^3 =
1^{ 8 } \cdot (-i) =
-i = -i $$ |
| ② | $$ i^{20} = i^{4 \cdot 5 + 0} =
\left( i^4 \right)^{ 5 } \cdot i^0 =
1^{ 5 } \cdot 1 =
1 $$ |
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