An example, using Manipulate
serie = ComplexExpand@ReIm@ReplaceAll[z -> \[Xi] + I \[Psi]][Accumulate[List @@ Normal@Series[Exp[z], {z, 0, 3}]]];
Manipulate[
expz = ReIm@Exp[First[z] + I Last[z]];
pts = serie /. {\[Xi] -> First[z], \[Psi] -> Last[z]};
Graphics[{
PointSize@Large,
Green, Point@expz,
Red, Point@pts
}, Axes -> True, PlotRange -> {{-2, 10}, {-2, 5}}
],
{{z, {1.5, 1}}, Locator},
{expz, None}, {pts, None}
]
