Project ForgeEngineering Mathematics
Complex Variables
GATE 2009
Medium
Using the residue theorem, the value of the integral (counterclockwise) ∮(8−7z)/(z−4) dz around a circle with center at z=0 and radius=8 is
- A−20πi
- B−40π
- −40πi
- D40πi
Explanation
The pole z=4 lies inside |z|=8. Residue=lim(z→4)(z−4)f(z)=8−7(4)=−20. Integral=2πi×(−20)=−40πi.
Source: GATE CH 2009 (2009)
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