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Possible Duplicate:
Manipulate Exp[I θ]+b Exp[-I θ]

Thought it might be best to add another question. Not sure my comment would be seen in the original question.

My question is: How do we add the curve Exp[I θ] + b Exp[-I θ] to the figure produced by this code?

Manipulate[
  With[{
    p1 = {Cos[θ], Sin[θ]},
    p2 = {b Cos[-θ], b Sin[-θ]},
    p3 = {(1 + b) Cos[θ], (1 - b) Sin[θ]}
   },
   Graphics[{
     Circle[{0, 0}],
     {Red, Circle[{0, 0}, b], Arrow[{{0, 0}, p1}], Arrow[{{0, 0}, p2}]},
     Arrow[{{0, 0}, p3}],
     {Dashed, Line[{p1, p3, p2}]},
     {Red, Text[E^(I "θ"), 1.1 p1], Text["b"/E^(I "θ"), 1.1 p2]},
     Tooltip[Point[p3], E^(I "θ") + "b"/E^(I "θ")]
    },
    PlotRange -> {{-#, #}, {-#, #}} &[1.5],
    BaseStyle -> 20,
    ImageSize -> 500]
   ],
  Grid[{
    {"b ", Control[{{b, 0.5, ""}, 0, 1, 0.1}], Dynamic[b]},
    {"θ", Control[{{θ, Pi / 4, ""}, 0, 2 Pi, 0.1}], Row[{Dynamic[θ 180` / Pi], Degree}]}
  }, BaseStyle -> 20]
]
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