A vector space over the complex numbers C has the same definition as a vector space over the reals except that scalars are drawn from C instead of from R. Show that each of these is a vector space over the complex numbers. (Recall how complex numbers add and multiply: (a₀ + a₁i) + (b₀ + b₁i) = (a₀ + b₀) + (a₁ + b₁)i and (a₀ + a₁i)(b₀ + b₁i) = (a₀b₀ - a₁b₁) + (a₀b₁ + a₁b₀)i.)

(a) The set of degree two polynomials with complex coefficients

(b) This set

Transcribed Image Text:

0 a a, b EC and a+