Q. Find the value of $\frac{i ^{4 n + 1} - i ^{4 n - 1}}{2}$ .

3312 214 Complex Numbers and Quadratic Equations Report Error

A

$i$

27%

B

$2 i$

31%

C

$- i$

25%

D

$- 2 i$

18%

Solution:

$\frac{i ^{4 n + 1} - i ^{4 n - 1}}{2}$
$= \frac{i ^{4 n} i - i ^{4 n} i ^{- 1}}{2}$
$= \frac{i ^{2} - 1}{2 i}$
$= \frac{- 2}{2 i}$
$= i$