Question
Answer
$$-12i^{24}+3i^{118}+8i^{53}-12i^{50}=8i-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-12i^{24}+3i^{118}+8i^{53}-12i^{50}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-12-3+8i+12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}8i-3\end{aligned} $$ | |
| ① | $$ -12i^{24} = -12 \cdot i^{4 \cdot 6 + 0} =
-12 \cdot \left( i^4 \right)^{ 6 } \cdot i^0 =
-12 \cdot 1^{ 6 } \cdot 1 =
-12 \cdot 1 $$ |
| ② | $$ 3i^{118} = 3 \cdot i^{4 \cdot 29 + 2} =
3 \cdot \left( i^4 \right)^{ 29 } \cdot i^2 =
3 \cdot 1^{ 29 } \cdot (-1) =
3 \cdot -1 = -3 $$ |
| ③ | $$ 8i^{53} = 8 \cdot i^{4 \cdot 13 + 1} =
8 \cdot \left( i^4 \right)^{ 13 } \cdot i^1 =
8 \cdot 1^{ 13 } \cdot i =
8 \cdot i $$ |
| ④ | $$ -12i^{50} = -12 \cdot i^{4 \cdot 12 + 2} =
-12 \cdot \left( i^4 \right)^{ 12 } \cdot i^2 =
-12 \cdot 1^{ 12 } \cdot (-1) =
-12 \cdot -1 = 12 $$ |
| ⑤ | Combine like terms: $$ 8i \color{blue}{-3} \, \color{red}{ -\cancel{12}} \,+ \, \color{red}{ \cancel{12}} \, = 8i \color{red}{-3} $$ |
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