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The residues of a complex function X(z)=(1-2z)/(z(z-1)(z-2)) at its poles are

1. (1)/(2),-(1)/(2) and 1
2. (1)/(2),(1)/(2) and -1
3. (1)/(2),1 and -(3)/(2)
4. (1)/(2),-1 and (3)/(2)

Correct answer: (1)/(2),1 and -(3)/(2)

Solution

For X(z)=(1-2z)/(z(z-1)(z-2)): residue at 0 = (1)/((-1)(-2))=1/2; at 1 = (1-2)/((1)(-1))=1; at 2 = (1-4)/((2)(1))=-3/2. So residues are 1/2, 1, -3/2 (index 2), not the stored option 3.

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