Question
Answer
$$(i^{35}+\dfrac{1}{i})^2+i^{100}=(-i+\dfrac{1}{i})^2+1$$
Explanation
| $$ \begin{aligned}(i^{35}+\frac{1}{i})^2+i^{100}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-i+\frac{1}{i})^2+1\end{aligned} $$ | |
| ① | $$ i^{35} = i^{4 \cdot 8 + 3} =
\left( i^4 \right)^{ 8 } \cdot i^3 =
1^{ 8 } \cdot (-i) =
-i = -i $$$$ i^{100} = i^{4 \cdot 25 + 0} =
\left( i^4 \right)^{ 25 } \cdot i^0 =
1^{ 25 } \cdot 1 =
1 $$ |
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