Discussion
Let a system be represented by :
\[ F(s) = \frac{s(s-1+j2)(s-1-j2)}{(s+2)(s+j1)(s-j1)} \]
Identify which one of the following do not define a zero ?
Answer: C
The value that does not define a zero is -2.
The zeros of F(s) are the values of s that make the numerator zero:
\[ s(s - 1 + j2)(s - 1 - j2) = 0 \]
so the zeros are s = 0, s = 1 - j2 and s = 1 + j2. The value -2 makes the factor (s + 2) in the denominator zero, so it is a pole, as are \(\pm j1\). The other three options are all zeros.
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