What is the "standard basis" for fields of complex numbers? What is the "standard basis" for fields of complex numbers?
For example, what is the standard basis for $\Bbb C^2$ (two-tuples of the form: $(a + bi, c + di)$)?  I know the standard for $\Bbb R^2$ is $((1, 0), (0, 1))$.  Is the standard basis exactly the same for complex numbers?
P.S. - I realize this question is very simplistic, but I couldn't find an authoritative answer online.

The "most standard" basis is also $\left\lbrace(1,0),\, (0,1)\right\rbrace$. You just take complex combinations of these vectors. Simple :)
