sol = Solve[z^5 == 32, z]

Table[ComplexExpand[Replace[z, sol[[n]]]], {n, 1, 5}]

ComplexExpand[(Exp[I x] + Exp[-I x])/
        2]

FullSimplify[
      Arg[(-1 + I Sqrt[3])/2] - 
        Arg[(1 + I)]  - 
        Arg[(-1 + I Sqrt[3])/
              2/(1 + I)]]

ArcTan[((1 + (Sqrt[3]))/(-1 + (Sqrt[3])))]

Solve[{x^2 + y^2 == 2, x == y}, {x, y}]

Table[Coefficient[(x + i)^i, x^j], {i, 0, 3}, {j, 1, 3}]

f[a_, b_, c_] := {5  a + b - c, -a + 2  c, 
        a + b + 7  c}
lis = {a, b, c}
m = Table[Coefficient[f[a, b, c], lis[[j]]], {j, 1, 3}]

CharacteristicPolynomial[m, x]
NullSpace[m]

p[x_] := -7 + 5 (x^2) - (x^3) + z - 5 x z + 
        (x^2) z

p[0]

LinearSolve[m, {1, 3, 2}]

m . {0, 1, 0}

Eigenvalues[m]

Eigenvectors[m]