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Find All Stationary Points for a Vector Field
Find all the stationary points for the dynamic system z(t)z(t)+sin(z(t)4).
In[1]:=

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roots = Reduce[

   Sin[z^4] + z == 0 && -2 <= Re[z] <= 2 && -2 <= Im[z] <= 2, z];
In[2]:=

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roots[[1 ;; 3]]
Out[2]=

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Show[StreamPlot[{Re[Sin[(x + I y)^4] + (x + I y)], 

   Im[Sin[(x + I y)^4] + (x + I y)]}, {x, -2, 2}, {y, -2, 2}], 

 ListPlot[{Re[z], Im[z]} /. {ToRules[roots]}, 

  PlotStyle -> Directive[PointSize[Medium], Red]]]
Out[3]=