Question
Answer
$$2^5(2i)^2 \cdot \dfrac{(2i^2)^2}{i^4}\cdot4^2=-8192$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2^5(2i)^2\frac{(2i^2)^2}{i^4}\cdot4^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}32\cdot4i^2\frac{(2i^2)^2}{i^4}\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}32\cdot(-4)\frac{(2i^2)^2}{i^4}\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-128 \cdot \frac{(2i^2)^2}{i^4}\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-128 \cdot \frac{4i^4}{1}\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-128\cdot\frac{4}{1}\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-128\cdot4\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}-512\cdot16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}-8192\end{aligned} $$ | |
| ① | $$ \left( 2i \right)^2 = 2^2i^2 = 4i^2 $$$$ \left( 2i \right)^2 = 2^2i^2 = 4i^2 $$$$ \left( 2i \right)^2 = 2^2i^2 = 4i^2 $$ |
| ② | $$ 4i^2 = 4 \cdot (-1) = -4 $$ |
| ③ | $$ 32 \cdot -4 = -128 $$ |
| ④ | $$ \left( 2i^2 \right)^2 = 2^2 \left( i^2 \right)^2 = 4i^4 $$ |
| ⑤ | $$ i^4 = i^2 \cdot i^2 =
( - 1) \cdot ( - 1) =
1 $$ |
| ⑥ | $$ 4i^4 = 4 \cdot i^2 \cdot i^2 =
4 \cdot ( - 1) \cdot ( - 1) =
4 $$ |
| ⑦ | Remove 1 from denominator. |
| ⑧ | $ -128 \cdot 4 = -512 $ |
| ⑨ | $ -512 \cdot 16 = -8192 $ |
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