Locus of z if  $\arg [z-(1+i)]=\{\begin{array}{l}\frac{3\pi }{4}when\left|z\right|<|z-2|\\ \frac{-\pi }{4}when\left|z\right|>|z-2|\end{array}$  is:

Lines passing through (2, 0) and (1, 1)

A set of two rays

A line segment

Straight lines passing through (2, 0)