Question

Solve :-$\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}$

Answer 1

$=\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}$

$=\frac{i^4+i^2+i^4+i^2+i^4}{i^2+i^4+i^2+i^4+i^2}$

$=\frac{3-2}{-3+2}$

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

$=-1$