Is $i \times 0 =0$?

Question

Is $i \times 0 =0$? That is $\sqrt{-1} \times 0 = 0$?,
I am asking this question because I could not make sense of why it is equal to 0

Please answer this and confirm. I know that this is a simple conceptual question. But this part of a proof.

Answer 1

Well, take a commutative ring $R$ or a field such as the complex numbers, then zero is absorbing.

Indeed, let $a\in R$. We have $0 = 0 + 0$ and so by multiplying with $a$, $0a = (0+0)a = 0a + 0a$. Adding $-0a$ (additive inverse of $0a$ with $0a + (-0a)=0$) gives $0 = 0a$.