You're solving for the unknowns 'a' and 'b'. Since (1 + i) is a root, the result must be zero once you sub it in. After subbing it in, you end up with a complex number which = 0.
For the complex number to = 0 + 0i, you must equate the real and unreal terms to find the values of 'a' and 'b' that satisfy it.