Question

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

• A. 0
• B. 2i
• C. -2i
• D. 2

Answer 1

Answer: (A)

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