Question

If $n$ is any positive integer, then the value of $\frac{i^{4n+1}-i^{4n-1}}{2}$ equals:

• A. $1$
• B. $-1$
• C. $i$
• D. $-i$

Answer 1

Answer: (C)

$i$

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

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

$=\frac{i-\frac{1}{i}}{2}$

$=\frac{i+i}{2}$

$=\frac{2i}{2}$

$=i$