determine the cartesian form and hence sketch the locus of z

Re(z)= l z l

given that l z-1+i l ≤ 1 find

a) the minimun and maximun value for l z l

b) the minimun and maximun value for arg (z)

given that l z-1+i l ≤ 2 and Re (z) ≥ 1 find

a) min and max value for l z l

b) min and maz value for arg (z)

thank you...