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The value of $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1=$
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The correct answer is:
$-2$
$\begin{aligned} & \frac{i^{584}\left(i^8+i^6+i^4+i^2+1\right)}{i^{574}\left(i^8+i^6+i^4+i^2+1\right)}-1=\frac{i^{584}}{i^{574}}-1 \\ & \quad=i^{10}-1=-1-1=-2\end{aligned}$
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