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Complex Integration — Howell & Matthews
Mathematics — Complex Analysis · cauchy-goursat-theorem
Problem Evaluate ∫ C ( 4 z 2 + 4 z − 3 ) − 1 d z = ∫ C ( 2 z − 1 ) − 1 ( 2 z + 3 ) − 1 d z \displaystyle\int_C (4z^2+4z-3)^{-1}\,dz = \int_C (2z-1)^{-1}(2z+3)^{-1}\,dz ∫ C ( 4 z 2 + 4 z − 3 ) − 1 d z = ∫ C ( 2 z − 1 ) − 1 ( 2 z + 3 ) − 1 d z C = C 1 + ( 0 ) C = C_1^+(0) C = C 1 + ( 0 ) C = C 1 + ( − 2 3 ) = { z : ∣ z + 2 3 ∣ = 1 } C = C_1^+\!\left(-\dfrac{2}{3}\right) = \left\{z : \left|z + \dfrac{2}{3}\right| = 1\right\} C = C 1 + ( − 3 2 ) = { z : z + 3 2 = 1 } C = C 3 + ( 0 ) C = C_3^+(0) C = C 3 + ( 0 ) Browse the problem library