sipka[z_,opts_]:=Graphics[{opts,{Arrowheads[Large],Arrow[{{0,0},{Re[z],Im[z]}}]}}];
Manipulate[Show[sipka[1+I,Hue[0],Dashed],sipka[(1+I)*Exp[I*fi],Hue[0.6]],PlotRange->{{-2,2},{-2,2}}],{fi,0,2*Pi}]