2. (2 pts) There is a theorem that states that if F() is analytic on a domain Rand F'() = (2), and a path C contained in

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2 2 Pts There Is A Theorem That States That If F Is Analytic On A Domain Rand F 2 And A Path C Contained In 1 (45.18 KiB) Viewed 30 times

2. (2 pts) There is a theorem that states that if F() is analytic on a domain Rand F'() = (2), and a path C contained in R has start point zla) and endpoint a(b), then Scf() = F(=(b)) - F(z(a)). Find an antiderivative for f() = x2 on the domain C and use the above theorem to check your answer to question 1.c. Name: Quiz 3, Prof. Coffman's Complex Analysis - Math 525 CALCULATORS OK Recall the definition: for an open domain RCC, and a curve with parametric equation : [a, b] → C, z(t) € R, the complex contour integral is defined as: dz Jeste)dz = L* 81201 $(2 1. Sketch the contour C and evaluate each of these contour integrals using the above definition to get an exact value. show work - partial credit for a decimal approximation. 2.5 pts each). a. 2(t) = e, osts 2 -dz b. z(t) = +it, 0 <t<2, 3 dz = c. C = line segment with start point 4+ 0i, end point 0 + 3i. Begin by stating any parametric expression z(t) for C. Sed ?dz