1. The problem statement, all variables and given/known data
In a youtube video() it is explained how gaussian beams propagate through an optical lens. Using the complex parameter q [itex] \frac{1}{q} = \frac{1}{R} - \frac{j\lambda}{\pi n w^2}[/itex] (with R the radius of curvature), one can use the ABCD matrix to calculate the effect of an optical system. Then it is explained how one can calculate the minimum waist [itex] w_0 [/itex] and at which position z this minimum waist occurs. But at 3.12 the position z for the minimum waist is given as:
[tex] z = \frac{Re[\frac{1}{q}]}{|\frac{1}{q}|^2} [/tex]

What I dont understand is that [itex] Re[\frac{1}{q}] = \frac{1}{R} [/itex] but the radius of curvature at [itex] w_0 [/itex] is supposed to be infinite so z is always zero.