Sin inverse of a complex number Is it possible to calculate the value of $\delta$ from the relation
$\delta=\sin^{-1}(5.4i)$ ? where $i=\sqrt{-1}$

Let $\delta=x+iy$
So, $\sin(x+iy)=5.4i$
Now, $\sin(x+iy)=\sin x\cos(iy)+\cos x\sin(iy)=\sin x\cosh y+i\cos x\sinh y$
Equating the real parts, $\sin x\cosh y=0\implies \sin x=0$ as $\cosh y\ge 1$ for real $y$
So, $\cos x=\pm1$
If $\cos x=1, x=2m\pi$ where $m$  is any integer 
and $\sinh y=5.4\implies \frac{e^y-e^{-y}}2=\frac{27}5\implies 5(e^y)^2-54e^y-5=0$ 
Solve for $e^y$ which is $>0$ for real $y$
If $\cos x=-1, x=2(n+1)\pi$ where $n$  is any integer 
and $\sinh y=-5.4\implies \frac{e^y-e^{-y}}2=-\frac{27}5\implies 5(e^y)^2+54e^y-5=0$ 
Solve for $e^y$ which is $>0$ for real $y$
