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