If z≠0 lies on the circle |z−1|=1and  ω =5/z,then ω lies on

z=5/ωand |z−1|=1⇒ 5ω−1=1⇒|ω−5|=|ω|that is, ω lies on the perpendicular bisector of the segment joining 0 and 5+0iTherefore ω lies on the straight line Re⁡(ω)=5/2