Locus of `z` if `arg[z - (1 + i)] = {(3pi)/4` when `|z|le|z-2| and (-pi)/4` when `|z| > |z-4|` is

Options

A. a striaght line passing through (2,0)
B. a straight line passing through (2,0) and (1,1)
C. a line segment
D. a set of two rays

Explanation

We have,
`rArr "arg"(z-(1+i))={{:((3pi)/4,"when"|z| le |z-2|),(-pi/4, "when"|Re(z) gt 1):}}`
`rArr` the locus of z is a set of two rays emanating from (1,1) as shown in Fig.