# Bug in FindRoot?

Manipulate[With[{sol=(Reap@FindRoot[Tan@z-(value[[1]]+I
start[[2]]),{z,start[[1]]+I
start[[2]]},StepMonitor:>Sow[z]])[[2,1]]//Flatten},
ComplexListPlot[sol,Joined->True,
PlotLabel->
"start: "<>ToString@Chop[start[[1]]+I start[[2]]]<>
"\nfirst iterate: "<>ToString@Chop@First@sol<>
"\nvalue of first iterate: "<>ToString@Chop@Tan@First@sol<>
"\nlast iterate: "<>ToString@Chop@Last@sol<>
"\nvalue of last iterate: "<>ToString@Chop@Tan@Last@sol<>
"\nvalue: "<>ToString[value[[1]]+I value[[2]]],
AspectRatio->1,PlotRange->All,ImageSize->300,PlotMarkers->Automatic,Epilog->{PointSize[Large],Blue,Point[First@ReIm@sol],Red,Point[Last@ReIm@sol]}]],
{start,{-5,-5},{5,5}},
{value,{-5,-5},{5,5}}
]


I notice that value and value of last iterate are always identical in the real part and always different in the imaginary part (sometimes "extreme", like 3.9I vs. -2.7I). I can't see how I would be treating real and imaginary parts differently in my code. Is that a bug in FindRoot, or do I have a bug in my code?

• if you see only a red dot in the middle it means that the FindRoot iteration got stuck (FindRoot::lstol). Can you help me get it unstuck and actually converge?
• is there a way to give the 2dim sliders some GridLines too?

Tan@z-(value[[1]]+I start[[2]])

Change this and it will work, except when FindRoot does not converge.