le an open disk in f. 5. a. Let 7 be a closedpath in [ and let be a connected open set in the complement of 7. Prove that as a function of 2 , Ind (2) =1 d's is constant on . ( You can use what we proved in class to answer this) b. Suppose @ is a connected open set in the complement of 7 as in part ( a) and in addition that @ is unbounded. Prove that for all z ED Ind, (2)=0. c. Let be the path as pictured: i.e. 7, is a closed path consisting of a semi circle and a closed interval on the real axis, where the semicircle is in the lower half plane IzEC Imaso, and where the semiorcle has radius R. What is Ind, ( i )? Explain your answer. 1 downMath 270- Assignment 3 P. 3 5. d. Let RS 1 and let up be the closed path as pictured, consisting of a semicircle of radius R and the closed interval, on the real axis [-R, RJ : Yup R R What is Ind, (i)? Justify your answer. 8 up Hint : What is Indy ( " ) + Ind (i )? up down