[SOLVED] Complex analysis, determine the set in the complex plane that satisfies...

I've been stuck for 3 days on this simple problem. I must graph the set of the complex plane where z satisfies . I've used the way of writing but reached a non sense condition for r. Well, the equation |3z+1|=1 would hold if . I really have no idea where I went wrong. I know there's likely an easy way to solve the problem, but still, I don't know where I'm wrong by replacing z for and then calculate the modulus of , etc.