If z = i , ,(2 - 3 ), then z = - Vidyadip

Question

If $z = i\,\log \,(2 - \sqrt 3 ),$ then $\cos z = $

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Answer

d
(d) Given, complex function $z = i\log (2 - \sqrt 3 ).$

The given equation may be written as

${e^{iz}} = {e^{{i^2}\log (2 - \sqrt 3 )}} = {e^{ - \log (2 - \sqrt 3 )}} = {e^{\log (2 - \sqrt 3 )}}^{ - 1}$

or ${e^{iz}} = (2 + \sqrt 3 ).$ Similarly, ${e^{ - iz}} = (2 - \sqrt 3 ).\,$
We know that

$\cos z = \frac{{{e^{iz}} + {e^{ - iz}}}}{2} = \frac{{(2 + \sqrt 3 ) + (2 - \sqrt 3 )}}{2} = 2.$

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