Question
Answer
$$-8i^{45}-12i^{12}-4i^{17}-5i^{63}=-7i-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-8i^{45}-12i^{12}-4i^{17}-5i^{63}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-8i-12-4i+5i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-7i-12\end{aligned} $$ | |
| ① | $$ -8i^{45} = -8 \cdot i^{4 \cdot 11 + 1} =
-8 \cdot \left( i^4 \right)^{ 11 } \cdot i^1 =
-8 \cdot 1^{ 11 } \cdot i =
-8 \cdot i $$ |
| ② | $$ -12i^{12} = -12 \cdot i^{4 \cdot 3 + 0} =
-12 \cdot \left( i^4 \right)^{ 3 } \cdot i^0 =
-12 \cdot 1^{ 3 } \cdot 1 =
-12 \cdot 1 $$ |
| ③ | $$ -4i^{17} = -4 \cdot i^{4 \cdot 4 + 1} =
-4 \cdot \left( i^4 \right)^{ 4 } \cdot i^1 =
-4 \cdot 1^{ 4 } \cdot i =
-4 \cdot i $$ |
| ④ | $$ -5i^{63} = -5 \cdot i^{4 \cdot 15 + 3} =
-5 \cdot \left( i^4 \right)^{ 15 } \cdot i^3 =
-5 \cdot 1^{ 15 } \cdot (-i) =
-5 \cdot -i = 5i $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-8i} \color{red}{-4i} + \color{red}{5i} -12 = \color{red}{-7i} -12 $$ |
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