Question
Answer
$$8i^{84}-8i^{25}-3i^{78}-3i^{112}=-8i+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8i^{84}-8i^{25}-3i^{78}-3i^{112}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8-8i+3-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-8i+8\end{aligned} $$ | |
| ① | $$ 8i^{84} = 8 \cdot i^{4 \cdot 21 + 0} =
8 \cdot \left( i^4 \right)^{ 21 } \cdot i^0 =
8 \cdot 1^{ 21 } \cdot 1 =
8 \cdot 1 $$ |
| ② | $$ -8i^{25} = -8 \cdot i^{4 \cdot 6 + 1} =
-8 \cdot \left( i^4 \right)^{ 6 } \cdot i^1 =
-8 \cdot 1^{ 6 } \cdot i =
-8 \cdot i $$ |
| ③ | $$ -3i^{78} = -3 \cdot i^{4 \cdot 19 + 2} =
-3 \cdot \left( i^4 \right)^{ 19 } \cdot i^2 =
-3 \cdot 1^{ 19 } \cdot (-1) =
-3 \cdot -1 = 3 $$ |
| ④ | $$ -3i^{112} = -3 \cdot i^{4 \cdot 28 + 0} =
-3 \cdot \left( i^4 \right)^{ 28 } \cdot i^0 =
-3 \cdot 1^{ 28 } \cdot 1 =
-3 \cdot 1 $$ |
| ⑤ | Combine like terms: $$ -8i+ \color{blue}{8} + \, \color{red}{ \cancel{3}} \, \, \color{red}{ -\cancel{3}} \, = -8i+ \color{red}{8} $$ |
This page was created using
Complex Expression calculator