On Jan 31, 11:28 pm, "C...@shaw.ca" <C...@shaw.ca> wrote: > > If z = r*e^(iw) [0 <= w , 2 pi], then 1/z = (1/r)e^(-iw), so Re(1/z) = > (1/r)cos(w), 0 <= w < 2 pi. Thus, if C is real and positive the curve > is r = cos(w)/C. As w goes from 0 to 2 pi this traces out two circles > of diameter 1/C, one centered at (1/2/C,0) and the other at (-1/2/C, > 0).
Ha?! Why don't you try it? If z traced the circle with center (-1/ (2C), 0) and radius 1/(2C), then the original equation Re(1/z) = C would be satisfied for z = -1/C. But Re(1/(-1/C)) = -C =/= C.