Question
Answer
$$i^{38}i^{45}=-i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{38}i^{45}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}i^{83} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i\end{aligned} $$ | |
| ① | $$ i^{38} i^{45} = i^{38 + 45} = i^{83} $$ |
| ② | $$ i^{83} = i^{4 \cdot 20 + 3} =
\left( i^4 \right)^{ 20 } \cdot i^3 =
1^{ 20 } \cdot (-i) =
-i = -i $$ |
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