z(a,b):=a+b*%i;

f(a,b):=sin(z(a,b))=1;

f(x,y);

r:realpart(f(x,y));

i:imagpart(f(x,y));

R: solve(r,y);

R;

Acosh(u):= log(u + sqrt(u^2-1));

y(x):=Acosh(1/sin(x))$ y(x);

I:solve(i,y);