Locus of `z` if `arg[z-(1+i)]` = `{:{(3pi//4 when |z| lt = |z-2|), (-pi//4 when |z|> |z-4|)}:}` is straight lines passing through (2, 0) straight lines passing through (2, 0) (1, 1) a line segment a set of two rays

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.