If $z = i^{i}$ , then find the value of $z - | z |$ .

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Solution

$z = i^{i} = (e^{i \frac{π}{2}})^{i} = e^{i \frac{π}{2} \times i} = e^{i^{2} \frac{π}{2}} = e^{- π / 2}$
$z - | z | = e^{- π / 2} - | e^{- π / 2} | = 0$

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