Question
Answer
$$i^{25}i^{14}=-i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{25}i^{14}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}i^{39} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i\end{aligned} $$ | |
| ① | $$ i^{25} i^{14} = i^{25 + 14} = i^{39} $$ |
| ② | $$ i^{39} = i^{4 \cdot 9 + 3} =
\left( i^4 \right)^{ 9 } \cdot i^3 =
1^{ 9 } \cdot (-i) =
-i = -i $$ |
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