Question
Answer
$$-8i^{29}-9i^{77}-5i^{100}-9i^{66}=-8i-9i-5+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-8i^{29}-9i^{77}-5i^{100}-9i^{66}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-8i-9i-5+9\end{aligned} $$ | |
| ① | $$ -8i^{29} = -8 \cdot i^{4 \cdot 7 + 1} =
-8 \cdot \left( i^4 \right)^{ 7 } \cdot i^1 =
-8 \cdot 1^{ 7 } \cdot i =
-8 \cdot i $$ |
| ② | $$ -9i^{77} = -9 \cdot i^{4 \cdot 19 + 1} =
-9 \cdot \left( i^4 \right)^{ 19 } \cdot i^1 =
-9 \cdot 1^{ 19 } \cdot i =
-9 \cdot i $$ |
| ③ | $$ -5i^{100} = -5 \cdot i^{4 \cdot 25 + 0} =
-5 \cdot \left( i^4 \right)^{ 25 } \cdot i^0 =
-5 \cdot 1^{ 25 } \cdot 1 =
-5 \cdot 1 $$ |
| ④ | $$ -9i^{66} = -9 \cdot i^{4 \cdot 16 + 2} =
-9 \cdot \left( i^4 \right)^{ 16 } \cdot i^2 =
-9 \cdot 1^{ 16 } \cdot (-1) =
-9 \cdot -1 = 9 $$ |
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