Final answer:
The zero of the transfer function H(s) = (1 + s) / (16 + s^2) is at s = -1. The poles are at s = 4i and s = -4i, which are complex conjugate poles.
Step-by-step explanation:
To find the zeros and poles of a transfer function, we first need to clarify the given transfer function. It seems there might be a typo in the question. A transfer function is typically given in the standard form H(s) = N(s) / D(s), where N(s) represents the numerator polynomial (zeros) and D(s) represents the denominator polynomial (poles). Assuming the transfer function is H(s) = (1 + s) / (16 + s^2), we can proceed.
To find the zeros of the transfer function, we set the numerator equal to zero: 1 + s = 0. This gives us a single zero at s = -1.
To find the poles of the transfer function, we set the denominator equal to zero: 16 + s^2 = 0. Solving for s, we get s = ± 4i, which means we have two complex conjugate poles at s = 4i and s = -4i.