Question
Answer
$$-4i^{22}-2i^{98}+3i^{57}+4i^{47}=-i+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-4i^{22}-2i^{98}+3i^{57}+4i^{47}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4+2+3i-4i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-i+6\end{aligned} $$ | |
| ① | $$ -4i^{22} = -4 \cdot i^{4 \cdot 5 + 2} =
-4 \cdot \left( i^4 \right)^{ 5 } \cdot i^2 =
-4 \cdot 1^{ 5 } \cdot (-1) =
-4 \cdot -1 = 4 $$ |
| ② | $$ -2i^{98} = -2 \cdot i^{4 \cdot 24 + 2} =
-2 \cdot \left( i^4 \right)^{ 24 } \cdot i^2 =
-2 \cdot 1^{ 24 } \cdot (-1) =
-2 \cdot -1 = 2 $$ |
| ③ | $$ 3i^{57} = 3 \cdot i^{4 \cdot 14 + 1} =
3 \cdot \left( i^4 \right)^{ 14 } \cdot i^1 =
3 \cdot 1^{ 14 } \cdot i =
3 \cdot i $$ |
| ④ | $$ 4i^{47} = 4 \cdot i^{4 \cdot 11 + 3} =
4 \cdot \left( i^4 \right)^{ 11 } \cdot i^3 =
4 \cdot 1^{ 11 } \cdot (-i) =
4 \cdot -i = -4i $$ |
| ⑤ | Combine like terms: $$ \color{blue}{3i} \color{blue}{-4i} + \color{red}{4} + \color{red}{2} = \color{blue}{-i} + \color{red}{6} $$ |
This page was created using
Complex Expression calculator