Talk:Equivalence of Definitions of Complex Inverse Hyperbolic Cosecant

As usual, the proof is correct. However, I feel compelled to address the usage of the verbosity:

$\sqrt{\left\vert{s}\right\vert} \left({\cos \left({\dfrac {\arg \left({s}\right)} 2}\right) + i \sin \left({\dfrac {\arg \left({s}\right)} 2}\right)}\right)$

when in the end, all that is done is expand $s^{1/2}$ to $\sqrt{\vert s\vert} e^{(i/2) \arg(s)}$. Which actually is an equivalent definition of the complex square root.

So why not cut these steps out from the proofs, and simply refer to the definition of complex square root in the exponential form? If you like, you can first put in $s = \vert s\vert e^{i \arg(s)}$ to make the use of the exponential form more explicit.

I feel this will add greatly to the clarity of the proofs, whose algebra currently may be a bit daunting to some of the readers. — Lord_Farin (talk) 10:16, 18 April 2014 (UTC)