i have a problem that states to find and simplify the polynomial function that has zeros of -3, 0, and 2i.
my current work:
f(x)=x(x+3)(x-2i)
f(x)=(x^2 + 3x)(x-2i)
f(x)=x^3 - 2ix^2 +3x^2 - 6xi
Just wanting to see if I am doing this problem in the correct way.
Does your problem forbid your function from having additional zeros? If it does no then you could try the function:
f(x)=x(x+3)(x-2i)(x+2i)
So
The advantage of this expression being that the coefficients are all real and it has all of the required zeros.