Question
Answer
$$9i^{72}-5i^8+11i^{57}+12i\cdot34=419i+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9i^{72}-5i^8+11i^{57}+12i\cdot34& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9i^{72}-5i^8+11i^{57}+408i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9-5+11i+408i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}419i+4\end{aligned} $$ | |
| ① | $$ 12 i \cdot 34 = 408 i $$ |
| ② | $$ 9i^{72} = 9 \cdot i^{4 \cdot 18 + 0} =
9 \cdot \left( i^4 \right)^{ 18 } \cdot i^0 =
9 \cdot 1^{ 18 } \cdot 1 =
9 \cdot 1 $$ |
| 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 | $$ 11i^{57} = 11 \cdot i^{4 \cdot 14 + 1} =
11 \cdot \left( i^4 \right)^{ 14 } \cdot i^1 =
11 \cdot 1^{ 14 } \cdot i =
11 \cdot i $$ |
| ⑤ | Combine like terms: $$ \color{blue}{11i} + \color{blue}{408i} + \color{red}{9} \color{red}{-5} = \color{blue}{419i} + \color{red}{4} $$ |
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