Question

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

• A. -1
• B. -1/2
• C. 1
• D. None of the above

Answer 1

The correct option is D None of the above

$z=ilog(2-\sqrt{3}i)$
$=ilog\left(2\right(1-\frac{\sqrt{3}}{2}i)$
let
$\omega =2-\sqrt{3}i$
$\omega =\sqrt{7}[\frac{2}{\sqrt{7}}-\sqrt{\frac{3}{7}}i]$
$\omega =\sqrt{7}{e}^{i\theta }$
Where $\theta =-ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$ilog\left(\omega \right)$
$=ilog(7{)}^{\frac{1}{2}}-\theta$
$z=ilog(7{)}^{\frac{1}{2}}+ta{n}^{-1}(\frac{\sqrt{3}}{2})$
Hence $cos\left(z\right)$ is none of the above.