Solve the quadratic equation: x² - x + (1 + i) = 0

Here a = 1, b = -1, c = 1 + i

Discriminant Δ = b² - 4ac

= (-1)² - 4(1)(1 + i)

= 1 - 4 - 4i

= -3 - 4i

Now, -3 - 4i = (2i - 1)²

∴ √Δ = ±(2i - 1)

Therefore, x = ^{1 ± (2i - 1)}/₂

Case 1: x = (1 + (2i - 1))/2 = (2i)/2 = i

Case 2: x = (1 - (2i - 1))/2 = (2 - 2i)/2 = 1 - i

Thus, the roots are: i and 1 - i