Q.The oxidation state of cobalt ion in the complex [Co(NH3)5Br]SO4 is

The coordination sphere of a complex is the central metal ion together with the ligands directly bonded to it, conventionally written inside square brackets as one discrete structural unit; when it carries a net charge it is called a complex ion, and any ionisable species written OUTSIDE the brackets are counter ions. Two related quantities describe a coordination sphere precisely. The coordination number (C.N.) of the central metal ion is the number of ligand DONOR ATOMS directly attached to it (not simply the number of ligand molecules/ions) -- for monodentate ligands this equals the ligand count, but for polydentate ligands each ligand contributes its own multiple donor atoms, so e.g. three bidentate en ligands ([Co(en)3]3+) give a coordination number of six, the same as six monodentate ligands would. The charge number of the complex ion is its overall net charge, calculated as (oxidation state of the metal) + (sum of all ligand charges); since the metal's oxidation state is one term of this sum, this same equation is routinely rearranged to back-calculate a metal's oxidation state once the complex ion's total charge and its ligands' individual charges are already known -- e.g. for [Fe(CN)6]4-, charge number -4 = O.S.(Fe) + 6x(-1), giving O.S.(Fe) = +2. Coordination number 6 always gives an octahedral geometry, while coordination number 4 gives either a square planar or a tetrahedral geometry (Werner's fourth postulate), which is why both quantities -- coordination number AND oxidation state -- are worked out together as the standard first step before analysing any complex's structure or bonding.