Question

$i^{57} + \frac{1}{i^{25}}$, when simplified has the value

• A. 0
• B. 2i
• C. -2i
• D. 2

Answer 1

Answer: (A)

0

Answer 2

$i^{57} + \frac{1}{i^{25}} = \left(i^{4}\right)^{14} . i + \frac{1}{\left(i^{4}\right)^{6} .i}$
$= i + \frac{1}{i} \left(\because i^{4} = 1\right)$
$= i - i \left(\because \frac{1}{i} = - i \right) = 0$