Question

Find a basis and the dimension of the following:
1. The set of all ordered pairs of complex numbers (Z1, Z2) over C.
2. The set of all order pairs of complex numbers (Z1, Z2) over R.

For 1):
a basis is {(1,0), (0,1)} and dim = 2
For 2):
a basis is {(1,0), (0,1), (i,0), (0,i)} and dim = 4

If anyone could verify/correct my answers it would be much appreciated. Thanks!

Answer 1

That is correct :)