The value of frac{i^{248}+i^{246}+i^{244}+i^{ | vedclass

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Question

(D) Given expression: $\frac{i^{248}+i^{246}+i^{244}+i^{242}+i^{240}}{i^{249}+i^{247}+i^{245}+i^{243}+i^{241}}$Factor out $i^{240}$ from the numerator

Vedclass · Accepted Answer

$-i$

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(D) Given expression: $\frac{i^{248}+i^{246}+i^{244}+i^{242}+i^{240}}{i^{249}+i^{247}+i^{245}+i^{243}+i^{241}}$Factor out $i^{240}$ from the numerator and $i^{241}$ from the denominator:$= \frac{i^{240}(i^8+i^6+i^4+i^2+1)}{i^{241}(i^8+i^6+i^4+i^2+1)}$Cancel the common term $(i^8+i^6+i^4+i^2+1)$:$= \frac{i^{240}}{i^{241}}$$= \frac{1}{i}$Multiply numerator and denominator by $i$:$= \frac{i}{i^2} = \frac{i}{-1} = -i$

The value of $\frac{i^{248}+i^{246}+i^{244}+i^{242}+i^{240}}{i^{249}+i^{247}+i^{245}+i^{243}+i^{241}}$,where $i=\sqrt{-1}$,is

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