Question
Answer
$$(4i)^{10}=-1048576$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4i)^{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1048576i^{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-1048576\end{aligned} $$ | |
| ① | $$ \left( 4i \right)^{10} = 4^{10}i^{10} = 1048576i^{10} $$ |
| ② | $$ 1048576i^{10} = 1048576 \cdot i^{4 \cdot 2 + 2} =
1048576 \cdot \left( i^4 \right)^{ 2 } \cdot i^2 =
1048576 \cdot 1^{ 2 } \cdot (-1) =
1048576 \cdot -1 = -1048576 $$ |
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