Project ForgeEngineering Mathematics
Complex Variables
GATE 2015
Hard
For complex variable z, evaluate (1/2πi)∮_C [e^(−2z)/(z(z−3))] dz along the CLOCKWISE contour |z|=2, rounded to 2 decimal places.
0.33(± 0.02 accepted)
Explanation
Only z=0 lies inside |z|=2 (z=3 is outside). Residue at z=0: e^0/(0−3)=−1/3. For a CLOCKWISE contour, the result is the negative of the standard (counterclockwise) residue sum: −(−1/3)=1/3=0.33.
Source: GATE CH 2015 (2015)
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