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Question

log (log i) =

A

$l o g \frac{π}{2}$

B

$l o g i \frac{π}{2}$

C

$l o g \frac{π}{2} + \frac{i π}{2}$

D

$l o g \frac{π}{2} - i \frac{π}{2}$

Medium

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Solution

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Correct option is C)

$i = e^{i π / 2}$
$lo g (lo g i) = lo g (lo g (e^{i π / 2}))$
$= lo g (i π / 2)$
$= lo g (π / 2 e^{i π / 2})$
$= lo g π / 2 + lo g e^{i π / 2}$
$= lo g π / 2 + i π / 2$

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