Manipulate[
       sol = Solve[N[BernoulliB[x, z] == 0, 10]];
       ListPlot[{{Re@z, Im@z} /. sol}] , {{x, 10}, 1, 100, 1}]

Manipulate[
       sol = Solve[N[BernoulliB[x, z] == 0, 10]];
       ListPlot[{{Re@z, Im@z} /. sol}] , {{x, 10}, 1, 100, 1}]

In case you meant to plot a range of n:

Manipulate[
     sol = Table[Solve[N[BernoulliB[n, z] == 0, 10]], {n, x, y}];
     ListPlot[ {Re@z, Im@z} /. sol]
       , {{x, 10}, 1, Dynamic[y], 1}, {{y, 12}, Dynamic[x], 100, 1}]