Question
Answer
$$2i^{16}-5i^{10}+7i^{28}=2+5+7$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2i^{16}-5i^{10}+7i^{28}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2+5+7\end{aligned} $$ | |
| ① | $$ 2i^{16} = 2 \cdot i^{4 \cdot 4 + 0} =
2 \cdot \left( i^4 \right)^{ 4 } \cdot i^0 =
2 \cdot 1^{ 4 } \cdot 1 =
2 \cdot 1 $$ |
| ② | $$ -5i^{10} = -5 \cdot i^{4 \cdot 2 + 2} =
-5 \cdot \left( i^4 \right)^{ 2 } \cdot i^2 =
-5 \cdot 1^{ 2 } \cdot (-1) =
-5 \cdot -1 = 5 $$ |
| ③ | $$ 7i^{28} = 7 \cdot i^{4 \cdot 7 + 0} =
7 \cdot \left( i^4 \right)^{ 7 } \cdot i^0 =
7 \cdot 1^{ 7 } \cdot 1 =
7 \cdot 1 $$ |
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