For $i^{2} = - 1$ find the value of $i^{253}$ .

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Solution

Given $i^{2} = - 1$ then $i^{4} = 1$ .

Now,

Let $Z = i^{253}$

$= (i^{4})^{63} . i$

$= 1. i$

$∴ Z = i$ .

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