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

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Question

(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

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(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: $= \frac{i^{584}(i^8 + i^6 + i^4 + i^2 + 1)}{i^{574}(i^8 + i^6 + i^4 + i^2 + 1)} - 1$ $= \frac{i^{584}}{i^{574}} - 1$ $= i^{584-574} - 1$ $= i^{10} - 1$ Since $i^2 = -1$,then $i^{10} = (i^2)^5 = (-1)^5 = -1$. $= -1 - 1 = -2$.

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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