Question

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

• A. 0
• B. 2 i
• C. -2i
• D. 2

Answer 1

The correct option is A 0

$i^{57}=i^{56}\times i=i^{4\times 14}\times i=i(i^{4\lambda }=1)$

$i^{25}=i^{24}\times i=i^{4\times 6}\times i=i(i^{4\lambda }=1)$

$\Rightarrow i^{57}+\frac{1}{i^{24}}=i+\frac{1}{i}=i+\frac{i}{i^2}=i-i=0$

$\Rightarrow Opt:\left(A\right)$ is the correct answer