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4

You can give explicit ranges as inputs to Solve Solve[{Sin[t] == 1/2, 0 <= t < 2 π}, t] (* {{t -> π/6}, {t -> (5 π)/6}} *)


2

Perhaps this is the sort of thing you want, shown here for your 2nd example: Plot3D[ReIm[Cos[\[Pi]*(1 - 2^-(a + b*I))]], {a, -3, 3}, {b, -3, 3}] Note that function ReIm is new as of Mathematica 10.1. If you're using an earlier version, you'll need to recreate the effect of that, e.g., by means of Through[{Re, Im}[ ....] ].



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