Find the value of:
$i^{i}$

0

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e^{- (4 n + 1) \frac{π}{2}}

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e^{(4 n + 1) \frac{1}{2}}

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1^{- (4 n + 1) \frac{π}{2}}

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Solution

The correct option is C $e^{- (4 n + 1) \frac{π}{2}}$

$i$ can be expressed as $e^{(i π / 2)}$

So, $i^{i}$ can be expressed as $(e^{(i π / 2)})^{i}$

Hence, $i^{i} = e^{[i^{(2)} \frac{π}{2}]}$

we know that $i ² = - 1$

$⟹ i^{i} = e^{(- π / 2)}$

So in general, $i^{i} = e^{- (2 n π + π / 2)} = e^{- (4 n + 1) \frac{π}{2}}$

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