Question
Answer
$$i^{25}+3i^{19}-2i^{10}+1=i-3i+2+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{25}+3i^{19}-2i^{10}+1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}i-3i+2+1\end{aligned} $$ | |
| ① | $$ i^{25} = i^{4 \cdot 6 + 1} =
\left( i^4 \right)^{ 6 } \cdot i^1 =
1^{ 6 } \cdot i =
i $$ |
| ② | $$ 3i^{19} = 3 \cdot i^{4 \cdot 4 + 3} =
3 \cdot \left( i^4 \right)^{ 4 } \cdot i^3 =
3 \cdot 1^{ 4 } \cdot (-i) =
3 \cdot -i = -3i $$ |
| ③ | $$ -2i^{10} = -2 \cdot i^{4 \cdot 2 + 2} =
-2 \cdot \left( i^4 \right)^{ 2 } \cdot i^2 =
-2 \cdot 1^{ 2 } \cdot (-1) =
-2 \cdot -1 = 2 $$ |
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