left|frac{1}{i^{2020}}+frac{2}{i^{2021}}+frac | vedclass

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(C) We know that $i^4 = 1$. Therefore,$i^{2020} = (i^4)^{505} = 1^{505} = 1$. Similarly,$i^{2021} = i^{2020} 	imes i = i$,$i^{2022} = i^{2020} 	imes

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$2 \sqrt{2}$

Vedclass · Answer

(C) We know that $i^4 = 1$. Therefore,$i^{2020} = (i^4)^{505} = 1^{505} = 1$. Similarly,$i^{2021} = i^{2020} 	imes i = i$,$i^{2022} = i^{2020} 	imes i^2 = -1$,and $i^{2023} = i^{2020} 	imes i^3 = -i$. Substituting these values into the expression: $\left|\frac{1}{1} + \frac{2}{i} + \frac{3}{-1} + \frac{4}{-i}ight|$ $= \left|1 - 2i - 3 + 4iight|$ $= \left|-2 + 2iight|$ $= \sqrt{(-2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$.

$\left|\frac{1}{i^{2020}}+\frac{2}{i^{2021}}+\frac{3}{i^{2022}}+\frac{4}{i^{2023}}\right|$ is equal to

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