This is LaTeX code:

[latex]
(z_1,z_2) = (a_1 + i b_1,a_2+i b_2) = (a_1 + i b_1, i a_1 + b_1) = (a_1, i a_1) + (i b_1, b_1) = a_1 (1,i) + b_1(i,1)
[/latex]