solve these using calculus

Show that R - R 2#+ iz R+ + R R2+R+1 2+z+1 R- 1)2 for all z satisfying |z| = R > 1.Now the mal part of the kit-hand mick lon in widenily and, in oracle find the wal partof the right-hand nits, we wrik that kicks in the for ap(-17) -2 12 which bacianix 1 The real part of this is clearly 7. Um complex rohn to prove the Law of Carin: Let AUK is a briangh with Hint: Pha Cal the origin, Haly, and A al ny Prove that\ffunction, /jmDinib domain SoFin,) =0bedin ElaineCiait HaimC, wokigh) = Furni Tang() in analytic in its domain Andwe have proved hal , () = Dixonal Theex fox, by the criquinom of analytic