Is the group $(\mathbb{C},+)=\langle1,i\rangle$? I'm trying to see if I understand the notation. I think that
$$(\mathbb{C},+)=\langle1,i\rangle$$
Is this true?

Since the group operation in question is addition, $\langle 1,i \rangle$ generates only the complex numbers with integer real and imaginary parts: $\mathbb{Z}[i]$. In fact, the additive group $\mathbb{C}$ is not finitely-generated: it cannot be generated by any finite subset.
If we think of $\mathbb{C}$ as a vector space over $\mathbb{R}$, then it is generated by the set $\{1,i\}$.
If we think of $\mathbb{C}$ as an unital algebra over $\mathbb{R}$, then it is generated solely by $i$.
