Answer
$$\frac{i^{18}-i}{5i-i^{16}}=\frac{-2+3i}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{i^{18}-i}{5i-i^{16}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-1-i}{5i-i^{16}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-1-i}{5i-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-2+3i}{13}\end{aligned} $$ | |
| ① | $$ i^{18} = i^{4 \cdot 4 + 2} =
\left( i^4 \right)^{ 4 } \cdot i^2 =
1^{ 4 } \cdot (-1) =
-1 = -1 $$ |
| ② | $$ -i^{16} = - i^{4 \cdot 4 + 0} =
- \left( i^4 \right)^{ 4 } \cdot i^0 =
- 1^{ 4 } \cdot 1 =
- 1 $$ |
| ③ | Divide $ \, -1-i \, $ by $ \, -1+5i \, $ to get $\,\, \dfrac{-2+3i}{13} $. ( view steps ) |
This page was created using
Complex Expression calculator