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

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Aicharya · Accepted Answer

$\begin{aligned} & \frac{i^{245}+i^{246}+i^{244}+i^{242}+i^{240}}{i^{243}+i^{247}+i^{245}+i^{243}+i^{241}} \ & =\frac{i^{240}\left(i^8+i^6+i^4+i^2+1ight)}{i^{241}\left(i^8+i^6+i^4+i^2+1ight)} \ & =\frac{i^{200}}{i^{241}} \ & =\frac{1}{i} \ & =\frac{i}{i^2}=-i\end{aligned}$

The value of…

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