How do I solve ODEs in the complex domain?

I want to solve the following ordinary differential equation dwdz = exp(-w) + sqrt(-exp(-2w)-1) on the complex domain, subject to the boundary condition w = i when z = i. I.e. w = phi+i*psi and z = x+i*y are complex and I want the solution on a specified grid in the argand plane. For this purpose I am first attempting to solve the simpler problem dwdz = w with same boundary condition for which I know the analytical answer to be w = i*exp(z-i). My tactic is to use some built in matlab ODE solver by looping through calls to say ode45 along a grid line in the argand plane. For example:

[z,w] = ode45(@(z,w) w,-10*1j:0.1*1j:10*1j,[1j 1j]);

here I am attempting to solve the ODE along the grid line which is the imaginary axis. But this doesn't seem to work as I get an error.

Is there any way to accomplish what I want in matlab and could anyone give suggestions with examples on how to do so? Thanks!