To solve for the $\sin^{-1} z$ ($z$ element of $\mathbb{C}$), the book reads that
$w = \sin^{-1} z$ when $z = \sin w$ implies:
$w = \sin^{-1} z$ when $z = (e^{iw} - e^{-iw})/2i$ implies:
$(e^{iw})^2 - 2iz(e^{iw}) - 1 = 0$ *
I don't see (2) implies (3). I mean it looks like the first step they used was mutiply out the $2i$, then subtract $2zi$ from both sides, but I'm lost after that.