Have a question:

Let f be the complex polynomial

f(x)=(3+i)x^2+(-2-6i)x+12

Calculate the following values f(i) and f(2+3i)

I calculated these values as such:

f(i)=(3+i)i^2+(-2-6i)i+12

Doing the math f(i)=15-3i

f(2+3i)=(3+i)(2+3i)(2+3i)+(-2-6i)(2+3i)+12

Doing the math f(2+3i)=-1+13i

Is this right?

Also, it then asks find a complex number z such that the equation f(x)=z has a unique solution (use the formula for solving a quadratic equation). How do you do this?