Answer:
±i
Step-by-step explanation:
Observing that the first two coefficients are the same as the last two, we can factor this function by grouping.
f(x) = (x^3 -7x^2) +(x -7) = x^2(x -7) +1(x -7)
f(x) = (x^2 +1)(x -7)
The factor x-7 has a real zero at x=7, so the complex zeros come from the quadratic factor (x^2 +1).
Setting that to zero and solving for x, we find ...
x^2 +1 = 0
x^2 = -1
x = ±√(-1) = ±i
The complex zeros are x = +i and x = -i.
