Question 24 (15 marks) From the fundamental theorem of algebra that we proved in class, it can be shown that ifza,...,zn_1 are the I: (not necessarilyr distinct] complex solutions to th- 2 z" + n_12\"'1 +an_2Z\"_ + ---+c1z+ co = El, 2" + on_1z\"_1 + en_2z"_2 + ---+ alz + on. = (z 20H: - 21} - - - [z - 2,1-1). [a] Find all 4 distinct complex solutions to the following equation: ('3) (c) z'+16=0. Denote by z.) and 21, respectively, the solution lying in the rst quadrant and the seoond quadrant. Denote the remaining 2 distinct solutions by 22 and 23. Let W) = 24:16' foIEz) = m Ma) = W Show that m) =1\") = foil). 2 _ 31 z - 30 For nn:,r real number R > 4, denote the circular arc from [13.0) to (-R. U) by 'm and denote the line from (-R.0) to [R.0) by 1'. Thus, LR starts where TR ends. We let 13L}; to denote the curve obtained by following We to its end and than continuing on L3 to its entt Thus, 73L}: is a closed (piecewise) C?1 come. See part (c} of Proposition 4.6 on P3. 57 of your textbook. You may make use of this Proposition too. Let C.) and Cl denote circles centered at In and 21, respectively, both traversed counter-clockwise Use the deformation theorem and part (b) to explain why / f(z)dz = M2) dz+ 11(2) dz. \"ml-R cc 2'. - .20 O; z _ :1