Question
Answer
$$-6i^{62}+10i^{113}-i^{22}-4i^{56}=10i+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-6i^{62}+10i^{113}-i^{22}-4i^{56}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6+10i+1-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}10i+3\end{aligned} $$ | |
| ① | $$ -6i^{62} = -6 \cdot i^{4 \cdot 15 + 2} =
-6 \cdot \left( i^4 \right)^{ 15 } \cdot i^2 =
-6 \cdot 1^{ 15 } \cdot (-1) =
-6 \cdot -1 = 6 $$ |
| ② | $$ 10i^{113} = 10 \cdot i^{4 \cdot 28 + 1} =
10 \cdot \left( i^4 \right)^{ 28 } \cdot i^1 =
10 \cdot 1^{ 28 } \cdot i =
10 \cdot i $$ |
| ③ | $$ -i^{22} = - i^{4 \cdot 5 + 2} =
- \left( i^4 \right)^{ 5 } \cdot i^2 =
- 1^{ 5 } \cdot (-1) =
- -1 = 1 $$ |
| ④ | $$ -4i^{56} = -4 \cdot i^{4 \cdot 14 + 0} =
-4 \cdot \left( i^4 \right)^{ 14 } \cdot i^0 =
-4 \cdot 1^{ 14 } \cdot 1 =
-4 \cdot 1 $$ |
| ⑤ | Combine like terms: $$ 10i+ \color{blue}{6} + \color{red}{1} \color{red}{-4} = 10i+ \color{red}{3} $$ |
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