Question
Answer
$$3i^5+9i^2-12i^{46}+8i^{105}=11i+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3i^5+9i^2-12i^{46}+8i^{105}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3i-9+12+8i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}11i+3\end{aligned} $$ | |
| ① | $$ 3i^5 = 3 \cdot i^{4 \cdot 1 + 1} =
3 \cdot \left( i^4 \right)^{ 1 } \cdot i^1 =
3 \cdot 1^{ 1 } \cdot i =
3 \cdot i $$ |
| ② | $$ 9i^2 = 9 \cdot (-1) = -9 $$ |
| ③ | $$ -12i^{46} = -12 \cdot i^{4 \cdot 11 + 2} =
-12 \cdot \left( i^4 \right)^{ 11 } \cdot i^2 =
-12 \cdot 1^{ 11 } \cdot (-1) =
-12 \cdot -1 = 12 $$ |
| ④ | $$ 8i^{105} = 8 \cdot i^{4 \cdot 26 + 1} =
8 \cdot \left( i^4 \right)^{ 26 } \cdot i^1 =
8 \cdot 1^{ 26 } \cdot i =
8 \cdot i $$ |
| ⑤ | Combine like terms: $$ \color{blue}{3i} + \color{blue}{8i} + \color{red}{12} \color{red}{-9} = \color{blue}{11i} + \color{red}{3} $$ |
This page was created using
Complex Expression calculator