x  =  {{0, 1}, {1, 0}};

y[
          n_] =  {{E^(2 Pi I/n), 0}, {0, 
            E^(-2 Pi I/n)}};

MatrixPower[ y[n], ]

a  =  {{0, 1}, {-1, 0}};

b =  {{0, I}, {I, 0}};

MatrixPower[b, ]

b  .  a

MatrixPower[ a, ]  .  b

Plot[Exp[x], {x,  -2, 2}]

Plot3D[
      Abs[Exp[x  +  I y]], {x,  -2, 2}, {y, -Pi, Pi}]

Plot3D[
      Arg[Exp[x  +  I y]], {x,  -2, 2}, {y, -Pi, Pi}]

Plot3D[Re[Exp[x  +  I y]], {x,  -2, 2}, {y, -Pi, Pi},  
      PlotRange  -> {-10, 10}]

ComplexExpand[ Sin[x  +  I y]]

Log[I]

Log[-1  +  0.00001 I]

Log[-1  -  0.00001 I]

Plot3D[
      Abs[Log[x  +  I y]], {x,  -1, 1}, {y, -1, 1}]

ContourPlot[
      Abs[Log[x  +  I y]], {x,  -1, 1}, {y, -1, 1}]

DensityPlot[
      Re[Log[x  +  I y]], {x,  -1, 1}, {y, -1, 1}]

I^I

Exp[I Log[I]]

N[%]

x[u_, 
          v_]  :=  (1 +  v/2 Cos[u/2]) Cos[
            u];
y[u_, 
          v_]  :=  (1  +  v/2 Cos[u/2]) Sin[
            u];
z[u_, v_]  :=  v/2 Sin[u/2];

ParametricPlot3D[ { x[u, v],  y[u, v],  z[u, v] },  {u, 0,  
        2 Pi},  {v, -1, 1}]