If $\sqrt{a + ib} = x + iy$,then the possible value of $\sqrt{a - ib}$ is

$\sqrt[3]{61 - 46\sqrt{5}} = $

The value of $\sqrt{12\sqrt{5} + 2\sqrt{55}}$ is:

If $\tanh^{-1}(x+iy) = \frac{1}{2} \tanh^{-1}\left(\frac{2x}{1+x^2+y^2}\right) + \frac{i}{2} \tan^{-1}\left(\frac{2y}{1-x^2-y^2}\right)$,where $x, y \in \mathbb{R}$,then $\tanh^{-1}(iy) =$

$\sqrt{12-\sqrt{68+48 \sqrt{2}}}$ is equal to :

$\sec h^{-1}\left(\frac{1}{2}\right)-\operatorname{cosec} h^{-1}\left(\frac{3}{4}\right)$ is equal to