Answer:
x^4 + 2x^3 + 3x^2 + 2x + 2 = 0
Step-by-step explanation:
The computation of the polynomial equation of the lowest degree is shown below
As we know that the complex roots would always arise in the conjucate pairs
As -i is a root, i is also a root
As -1 + i is a root
And, -1 is also a root
Now the polynomial equation would be
(x + i)(x - i)(x + 1 - i)(x + 1 - i) = 0
(x^2 - i^2)[(x + 1)^2 - i^2] = 0
(x^2 + 1)[(x + 1)^2 + 1] = 0
(x^2 + 1)(x^2 + 2x + 2) = 0
x^4 + 2x^3 + 3x^2 + 2x + 2 = 0
