Question

If $z=ilog(2-\sqrt{3})$ then $\cos z=$

• A. i
• B. 2i
• C. 1
• D. 2

Answer 1

The correct option is D 2

$\cos z=\frac{e^{iz}+e^{-iz}}{2}$
$\therefore \cos \left[i\log (2-\sqrt{3})\right]=\frac{e^{i^2\log (2-\sqrt{3})}+e^{-i^2\log (2-\sqrt{3})}}{2}$
$\therefore \cos z=\frac{e^{-\log (2-\sqrt{3})}+e^{\log (2-\sqrt{3})}}{2}$
$\cos z=\frac{\frac{1}{2-\sqrt{3}}+(2-\sqrt{3})}{2}$

$\cos z=\frac{2+\sqrt{3}+2-\sqrt{3}}{2}$

$\cos z=2$