z^2 - z = 5 + 5i
z^2 - z + 1/4 = 5 + 5i + 1/4
(z - 1/2)^2 = 21/4 + 5i
z - 1/2 = ±√(21/4 + 5i)
z = 1/2 ± (5/2 + i)
z1 = 1/2 + 5/2 + i = 3 + i
z2 = 1/2 - 5/2 - i = - 2 - i
Product of roots :
(3 + i)(- 2 - i) = - 5 - 5i
The real part of the product of the roots is - 5