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Complex Integration — Howell & Matthews
Mathematics — Complex Analysis · cauchy-goursat-theorem
Problem Suppose that f ( z ) = u ( r , θ ) + i v ( r , θ ) f(z) = u(r,\theta) + iv(r,\theta) f ( z ) = u ( r , θ ) + i v ( r , θ ) z = r e i θ z = re^{i\theta} z = r e i θ ∫ 0 2 π [ u ( r , θ ) cos θ − v ( r , θ ) sin θ ] d θ = 0. \int_0^{2\pi} \left[u(r,\theta)\cos\theta - v(r,\theta)\sin\theta\right]d\theta = 0. ∫ 0 2 π [ u ( r , θ ) cos θ − v ( r , θ ) sin θ ] d θ = 0. f f f C 1 + ( 0 ) C_1^+(0) C 1 + ( 0 ) Browse the problem library