This is just a
system of linear equations and there are many ways to solve it. Even without knowing basically anything, you could just solve for z in the first equation, leading to
1) z = i - (1+i)w
plug the above into the second equation
2) (1-i)(i - (1+i)w) + iw =1
and solve for w. Then, you plug the w solution into 1) to get z.
