Question
Answer
$$i^{30}-i^{15}+i=2i-1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{30}-i^{15}+i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-1+i+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2i-1\end{aligned} $$ | |
| ① | $$ i^{30} = i^{4 \cdot 7 + 2} =
\left( i^4 \right)^{ 7 } \cdot i^2 =
1^{ 7 } \cdot (-1) =
-1 = -1 $$ |
| ② | $$ -i^{15} = - i^{4 \cdot 3 + 3} =
- \left( i^4 \right)^{ 3 } \cdot i^3 =
- 1^{ 3 } \cdot (-i) =
- -i = i $$ |
| ③ | Combine like terms: $$ \color{blue}{i} + \color{blue}{i} -1 = \color{blue}{2i} -1 $$ |
This page was created using
Complex Expression calculator