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