1. The problem statement, all variables and given/known data . I want to prove that there is one solution for e^z-z in every shifted copy of the fundamental strip by applying the argument principle to the boundary of a rectangle −M≤Rez≤M , 2kπi≤Imz≤2(k+1)πi for large M and integer k . I need help in using the argument principle here. 2. Relevant equations Argument principle. 3. The attempt at a solution I tried to compute the integral of the logarithmic derivative along the boundary of the square,but i'm stuck with it.