atan2alt(v,u)
ans = 

function Z = atan2alt(V,U)
  Z = -1i*log((U+1i*V)./sqrt(U.^2+V.^2));
  realInputs = (imag(U) == 0) & (imag(V) == 0);
  Z(realInputs) = real(Z(realInputs));
As I am editing this post, I see the expected symbolic display in the nice form as have grown to love. However, when I save the post, it does not display. (In fact, it shows up here in the discussions post.) This seems to be a new problem, as I have not seen that failure mode in the past.
You can see the problem in this Answer forum response of mine, where it did fail.