Project ForgeEngineering Mathematics
Calculus
GATE 2021
Hard
Let C represent the unit circle centered at the origin in the complex plane, z=x+iy. The value of the contour integral ∮_C [cosh(3z)/(2z)] dz (counter-clockwise) is
- A0
- B2
- πi
- D2πi
Explanation
f(z) = cosh(3z)/(2z) has a simple pole at z=0 (inside the unit circle), with residue = cosh(0)/2 = 1/2. By the residue theorem, the contour integral = 2πi × residue = 2πi × (1/2) = πi.
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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