Question

Value of $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1$ is

• A. -2
• B. 0
• C. -1
• D. 1

Answer 1

Answer: (A)

Given expression
$=\frac{i^{10}\left(i^{582}+i^{580}+i^{578}+i^{576}+i^{574}\right)}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1$
$=i^{10}-1={\left(i^2\right)}^5-1=(-1{)}^5-1=-1-1=-2$