$\sinh^{-1}\left(2^{3/2}\right)$ is equal to :

If $\cosh ^{-1} x = 2 \log _e(\sqrt{2}+1)$,then $x=$

If the value of $\sqrt{-5-12 i}+\sqrt{7+24 i}$ is a negative real number $k$,then $k=$

$\sqrt{(-3+4 i)(8+6 i)} = ?$

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 $\tanh^{-1}(iy) =$

$\operatorname{sech}^{-1}\left(\frac{3}{5}\right)-\tanh ^{-1}\left(\frac{3}{5}\right)=$