The question is describe the locus of Im (z+1/z) = 0
i.e.
http://www4c.wolframalpha.com/Calculate/MSP/MSP241519hba1388d3fa64f0000271d633fhbhh358f?MSPStoreType=image/gif&s=33&w=94&h=36
Now, the obvious method is to let z + x+iy and after a couple of lines of working you arrive at the answer...