A=(({{4, 3, 15}, {1, 1+I, 5}, {-8, -2, 22}}));
n=3;
showMarkers=False;
showRectangle=Thin;
eval=Eigenvalues[A]//N
evec=Abs[Eigenvectors[A]]//N

circles=Table[
Circle[{Re[A[[i,i]]],Im[A[[i,i]]]},Total[Abs[A[[i,Cases[Range[1,n],x_/;x≠i]]]]]],
{i,1,n}]

circleCentres=Table[
Callout[
{Re[A[[i,i]]],Im[A[[i,i]]]},
Subscript["a",ToString[i]<>ToString[i]]
],
{i,1,n}]

evalPoints=Table[
Callout[
{Re[eval[[i]]],Im[eval[[i]]]},
Subscript["λ",i],
{Re[eval[[i]]]-0.8,Im[eval[[i]]]+0.8}
],
{i,1,n}]//N

rangeRe=Flatten[{Re[Diagonal[A]]+circles[[;;,2]],Re[Diagonal[A]]-circles[[;;,2]]}]

rangeIm=Flatten[{Im[Diagonal[A]]+circles[[;;,2]],Im[Diagonal[A]]-circles[[;;,2]]}]

{Min[rangeRe],Max[rangeRe]}

{Min[rangeIm],Max[rangeIm]}

Show[
ListPlot[({{\[Piecewise], ({{circleCentres, showMarkers}, {(#1[[1]])&/@circleCentres, True}})}}),
PlotRange->{{-20,40},{-20,20}},
PlotStyle->,
PlotMarkers->{"◆",14},
AxesLabel->{"Re","Im"},
ImageSize->Large,
BaseStyle->{FontSize->14},
AspectRatio->Automatic
],
ListPlot[({{\[Piecewise], ({{evalPoints, showMarkers}, {(#1[[1]])&/@evalPoints, True}})}}),PlotStyle->,PlotMarkers->{"●",12}],
Legended[
Graphics[
{
,Thickness[0.004],circles,
Opacity[0.1],Disk@@@circles
}
]
,
PointLegend[{,},{"Circle centre","Eigenvalue"},LegendMarkerSize->14,LegendMarkers->{{"◆",14},{"●",11}}]
],
Graphics[{FaceForm[None],EdgeForm[showRectangle],Rectangle[{Min[rangeRe],Min[rangeIm]},{Max[rangeRe],Max[rangeIm]}]}]
]