1. The problem statement, all variables and given/known data a. Determine the complex potential for two equal counter-rotating vortices with strength [itex]\Gamma[/itex], the positive one located at z=-a and the negative one at z=a. b/ Show the shape of the streamlines for this case. 2. Relevant equations z = x + iy = r*e^(i[itex]\theta[/itex]) W(z) = [itex]\Phi[/itex] + i[itex]\Psi[/itex] where [itex]\Phi[/itex] is the potential function and [itex]\Psi[/itex] is the stream function 3. The attempt at a solution a. This part is relatively easy. I know that the complex potential for a vortex at the origin is i[itex]\Gamma[/itex]/(2*[itex]\pi[/itex]) * ln(z) Therefore, for the two vortices, we will have: W(z) = i[itex]\Gamma[/itex]/(2*[itex]\pi[/itex]) * ln((z+a)/(z-a)) b. This is where I start to have trouble. I need to separate W(z) into the real and imaginary parts, and then I know that the imaginary part is the stream function. However, I don't know how to do this. It is easy for a vortex at the origin, because then I would have ln(z) = ln(r*e^(i[itex]\theta[/itex])) = ln(r) + i[itex]\theta[/itex] However, the addition and subtraction of 'a' inside of the log is giving me a lot of trouble. I've tried to separate it every way that I can think of but haven't had any success. Any help would be much appreciated. Thanks!