Question

Find all zeros of the function f(x) = (x - 4)(x + 3)(x + (4 + 3i))(x - (4 - 3i)).

Is it x = 4, -3, -4 - 3i, and 4 - 3i ?

Answer 1

Yes they are the zeros :)
if we put x=4 the 1st factor becomes 0, making the whole function = 0.
Hoped it helped!

Answer 2

While your answer is correct, I suspect a typo in the problem, since the expanded polynomial does not have real coefficients:

x^4 - (1-6i)x^3 - (37+6i)x^2 + (25-72i)x + 300