Question

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

• A. $-1$
• B. $-\frac{1}{2}$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

$z=i\log (2-\sqrt{3})$
$\Rightarrow e^{iz}=e^{i^2\log (2-\sqrt{3})}=e^{\log (2+\sqrt{3})}=2+\sqrt{3}$
$\therefore \cos z=\frac{e^{iz}+e^{-iz}}{2}=\frac{(2+\sqrt{3})+(2-\sqrt{3})}{2}=2$