You can use the relationships of roots and coefficients to find the values of 'a' and 'b'.
The Sum Of Roots:
(a + bi) + (a - bi) + (a + 2bi) + (a - 2bi) = -4
a + bi + a - bi + a + 2bi + a - 2bi = -4
4a = -4
a = -1
The Product Of Roots:
(a + bi) (a - bi) (a + 2bi) (a - 2bi) = 10
(a^2 + b^2)...