Question

What is the value of i^-999? ​

Answer 1

Given :

•what is the value of $\rm{i^{-999}}$

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To find :

$\bf \diamondsuit the \: value \: of \: {i}^{ - 999} =$

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Values :

$\red\bigstar \sf {i}^{2} = - 1 \\ \\ \red \bigstar \sf \: {i}^{1} = i \\ \\ \: \red \bigstar \sf \: {i}^{3} = {i}^{2} i = - i \\ \\ \red \bigstar \sf {i}^{4} = ({ {i}^{2} })^{2} = 1$

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Solution :

On dividing 999 by 4 we obtain 3 as the remain

$\\ \therefore \sf {i}^{ - 999} = \frac{1}{ {i}^{999} } = \frac{1}{ {i}^{3} } = \frac{i}{ {i}^{4} } \\ \\ \implies \sf \: \frac{i}{ {i}^{4} } = \frac{i}{1} = i$

The answer will be i