Correct Phase (Bode) plot of transfer function
Any complex number \$Z\$ can be represented in rectangular coordinates or polar coordinates
$$Z = x + jy = A\angle\phi$$ 
where, \$A = \sqrt{x^2+y^2}\$ and \$\phi = atan2(y,x)\$ where, \$atan2(y,x)\$ is defined as



As you can see your conversion formula is valid only if \$x&gt;0\$.
Hence \$\phi\$ for \$a+jb\$ and \$\phi\$ for \$-a-jb\$ will be different.
I think this solves your problem.