MCQ
If $z = i\,\log \,(2 - \sqrt 3 ),$ then $\cos z = $
- A$i$
- B$2\, i$
- C$1$
- ✓$2$
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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