Question
Answer
$$i^{3217}-i^{427}+i^{18}=i+i-1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{3217}-i^{427}+i^{18}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}i+i-1\end{aligned} $$ | |
| ① | $$ i^{3217} = i^{4 \cdot 804 + 1} =
\left( i^4 \right)^{ 804 } \cdot i^1 =
1^{ 804 } \cdot i =
i $$ |
| ② | $$ -i^{427} = - i^{4 \cdot 106 + 3} =
- \left( i^4 \right)^{ 106 } \cdot i^3 =
- 1^{ 106 } \cdot (-i) =
- -i = i $$ |
| ③ | $$ i^{18} = i^{4 \cdot 4 + 2} =
\left( i^4 \right)^{ 4 } \cdot i^2 =
1^{ 4 } \cdot (-1) =
-1 = -1 $$ |
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