Is $\{(a, b, c) \in \mathbb{C}^3 : a^3 = b^3\}$ a subspace of $\mathbb{C}^3$ I have two questions to solve:


Is $\{(a, b, c) \in \mathbb{R}^3 : a^3 = b^3\}$ a subspace of $\mathbb{R}^3$?
Is $\{(a, b, c) \in \mathbb{C}^3 : a^3 = b^3\}$ a subspace of $\mathbb{C}^3$?


For the first one, I proved it is. Then for the second part, I found almost no difference. So I am not sure if I am on the right track. I mean, I believe there must be some differences. But I can't figure it out.
Try with $(e^{i\frac{π}{3}} , -1,0)$ and $(1,1,0)$.
It's sum won't satisfy the property $a^{3}=b^{3}$
Try with $(e^{i\frac{π}{3}} , -1,0)$ and $(1,1,0)$.
It's sum won't satisfy the property $a^{3}=b^{3}$