1. The problem statement, all variables and given/known data z + 1/z is it analytic? 2. Relevant equations du/dx = dv/dy and du/dy = -dv/dx where f = u+iv 3. The attempt at a solution I'm pretty sure I did this correctly, but I ran into an unexpected answer in a more complex problem using the same method and thought I'd ask about the easier question to make sure I'm doing this correctly. So my attempted solution was this: I expanded z to be x+iy, so z + 1/z = (x+iy) + (x+iy)^-1 I found du/dx = 1 + -(x+iy)^-2 dv/dy = i + -i(x+iy)^-2 du/dy = 0 -dv/dx = 0 So, according to my solution, the function is not analytic. What I think could be wrong is my answer to dv/dy. The derivative of iy in terms of y should just be i is what I think but for some reason I'm second guessing that. Thanks.