Question
Answer
$$(2i)^{12}=4096$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2i)^{12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4096i^{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4096\end{aligned} $$ | |
| ① | $$ \left( 2i \right)^{12} = 2^{12}i^{12} = 4096i^{12} $$ |
| ② | $$ 4096i^{12} = 4096 \cdot i^{4 \cdot 3 + 0} =
4096 \cdot \left( i^4 \right)^{ 3 } \cdot i^0 =
4096 \cdot 1^{ 3 } \cdot 1 =
4096 \cdot 1 $$ |
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