Question
Answer
$$9i^2-5i^8+11i^{5712}i^{34}=-9-5-11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9i^2-5i^8+11i^{5712}i^{34}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9i^2-5i^8+11i^{5746} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-9-5-11\end{aligned} $$ | |
| ① | $$ 11 i^{5712} i^{34} = 11 i^{5712 + 34} = 11 i^{5746} $$ |
| ② | $$ 9i^2 = 9 \cdot (-1) = -9 $$ |
| ③ | $$ -5i^8 = -5 \cdot i^{4 \cdot 2 + 0} =
-5 \cdot \left( i^4 \right)^{ 2 } \cdot i^0 =
-5 \cdot 1^{ 2 } \cdot 1 =
-5 \cdot 1 $$ |
| ④ | $$ 11i^{5746} = 11 \cdot i^{4 \cdot 1436 + 2} =
11 \cdot \left( i^4 \right)^{ 1436 } \cdot i^2 =
11 \cdot 1^{ 1436 } \cdot (-1) =
11 \cdot -1 = -11 $$ |
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