Question: Show that (𝛼 + 𝛽) + 𝜆 = 𝛼 + (𝛽 + 𝜆) for all 𝛼, 𝛽, 𝜆 ∈ 𝐂.
Answer: Let $\alpha = a + ib$, $\beta = c + id$ and $\lambda = e + if$ be given.
Then, $$ (\alpha + \beta) + \lambda = ((a + ib) + (c + id)) + (e + if) = ((a + c) + e) + i((b + d) + f) = (a + (c + e)) + i(d + (b + f)) = \alpha + (\beta + \lambda) $$
Where the middle equalites come from the properties of $\mathbb{R}$.