The value of frac{i^{592}+i^{590}+i^{588}+i^{ | vedclass

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(B) Given expression: $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1$ Factor out $i^{584}$ from the numera

Vedclass · Accepted Answer

$-2$

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(B) Given expression: $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1$ Factor out $i^{584}$ from the numerator and $i^{574}$ from the denominator: $\frac{i^{584}(i^8+i^6+i^4+i^2+1)}{i^{574}(i^8+i^6+i^4+i^2+1)}-1$ Cancel the common term $(i^8+i^6+i^4+i^2+1)$: $\frac{i^{584}}{i^{574}}-1 = i^{584-574}-1 = i^{10}-1$ Since $i^4 = 1$,$i^{10} = (i^4)^2 	imes i^2 = 1^2 	imes (-1) = -1$ Therefore,$-1 - 1 = -2$

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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