Creating a random complex univariate polynomial

Question

I am a newbie in Mathematica, but I need to create a random univariate polynomial of degree d with complex coefficients whose entries are random complex variables with real and imaginary parts being independent distributions with mean value = 1 and variance = 2.

Answer 1

Using FromDigits as suggested by J.M.

f[d_Integer, var_Symbol] := ExpandAll@FromDigits[
   (#1 + #2 I) & @@@ Transpose[{
      RandomVariate[NormalDistribution[1, Sqrt[2]], d]
      , RandomVariate[GammaDistribution[1/2, 2], d]
      }], var]

To figure out parameters of GammaDistribution

{α, β} /. 
 First@Solve[{Variance[GammaDistribution[α, β]] == v, 
    Mean[GammaDistribution[α, β]] == 
     m}, {α, β}]

 {m^2/v, v/m}

Answer 2

Just post anothor method about building a polynomial,and the coefficients you can use the @rhermans 's solution to produce.

list = RandomComplex[{-2 - I, 5 + 3 I}, 3]
(*{1.83992 + 1.75346 I,3.79133 + 1.05147 I, -0.0638321 - 0.551983 I}*)

AlgebraicNumber[x, list]
(*(1.83992 +1.75346 I) + (3.79133 + 1.05147 I) x - (0.0638321 + 0.551983 I) x^2*)