Question
Answer
$$i^{60}-i^{112}+10i^{93}-6i^{36}=10i-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{60}-i^{112}+10i^{93}-6i^{36}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}1-1+10i-6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}10i-6\end{aligned} $$ | |
| ① | $$ i^{60} = i^{4 \cdot 15 + 0} =
\left( i^4 \right)^{ 15 } \cdot i^0 =
1^{ 15 } \cdot 1 =
1 $$ |
| ② | $$ -i^{112} = - i^{4 \cdot 28 + 0} =
- \left( i^4 \right)^{ 28 } \cdot i^0 =
- 1^{ 28 } \cdot 1 =
- 1 $$ |
| ③ | $$ 10i^{93} = 10 \cdot i^{4 \cdot 23 + 1} =
10 \cdot \left( i^4 \right)^{ 23 } \cdot i^1 =
10 \cdot 1^{ 23 } \cdot i =
10 \cdot i $$ |
| ④ | $$ -6i^{36} = -6 \cdot i^{4 \cdot 9 + 0} =
-6 \cdot \left( i^4 \right)^{ 9 } \cdot i^0 =
-6 \cdot 1^{ 9 } \cdot 1 =
-6 \cdot 1 $$ |
| ⑤ | Combine like terms: $$ 10i \, \color{blue}{ -\cancel{1}} \,+ \, \color{green}{ \cancel{1}} \, \color{green}{-6} = 10i \color{green}{-6} $$ |
This page was created using
Complex Expression calculator