Why isn't the maximum argument of this loci pi/2?

Question

Why isn't the maximum argument $-\pi/2$ ? Where it is tangential to the imaginary axis as this seems a larger argument that -0.330? Thanks

Answer 1

Maximum argument means largest (most positive).

Clearly $-\frac{\pi}{2}$ is the minimum argument, not the maximum as it is the most negative, and hence the smallest.