Form a polynomial degree 4; zeros: -2+2I; -3 multiplicity 2

Question

I am so confused

Answer 1

These are your zeros.

 

x₁ = -2 - 2i

x₂ = -2 + 2i

x₃ = -3

x₄ = -3

 

The first two zeros are conjugates because they are complex.  The last two repeat.

 

So your function is

 

f(x) = (x + [2 + 2i])(x + [2 - 2i])(x + 3)(x + 3)

 

f(x) = (x² + x(2 - 2i) + x(2 + 2i) + (4 + 4))(x² + 6x + 9)

 

f(x) = (x² + 4x + 8)(x² + 6x + 9)