To prove that (α + β) + λ = α + (β + λ) for all α, β, λ ∈ ℂ (the set of complex numbers), we need to use the properties of complex number addition. Let α = a + bi, β = c + di, and λ = e + fi, where a, b, c, d, e, and f are real numbers. First, we calculate the left-hand side (LHS) of the equation: (α + β) + λ = ((a + bi) + (c + di)) + (e + fi) = (a + c + (b + d)i) + (e + fi) (using the addition property of complex numbers) = (a + c + e) + (b + d + f)i Next, we calculate the right-hand side (RHS) of the equation: α + (β + λ) = (a + bi) + ((c + di) + (e + fi)) = (a + bi) + (c + e + (d + f)i) (using the addition property of complex numbers) = (a + c + e) + (b + d + f)i Since the real and imaginary parts of the LHS and RHS are equal, we can conclude that: (α + β) + λ = α + (β + λ) Therefore, the equality (α + β) + λ = α + (β + λ) holds true for all α, β, λ ∈ ℂ, which proves the associative property of complex number addition.