complex ion
When you dissolve table salt, sodium and chloride simply drift apart as separate ions. But dissolve some metal salts and something different happens: the metal does not float around alone — it travels as a single charged package, a metal surrounded by a fixed entourage of attached groups that move with it as one unit. That package is a complex ion.
Precisely, a complex ion is a charged coordination entity: a central metal ion bonded to a definite set of ligands, the whole thing carrying a net electric charge. Its overall charge is the metal's oxidation state plus the charges of all the ligands. For [Co(NH3)6]3+, cobalt is +3 and the six ammonia ligands are neutral, so the ion is 3+. For [Fe(CN)6]4-, iron is +2 and six cyanide ligands are each 1-, giving 2 + (6 x -1) = -4. Inside the square brackets the metal and its ligands act as one species — in solution the cyanides do not wander off; the ion diffuses, conducts, and crystallizes as a whole. Outside the brackets sit counter-ions that balance this charge but are not part of the complex.
Complex ions matter because they are how metals actually exist in most real solutions — in water a 'bare' metal cation is really an aqua complex such as [Fe(H2O)6]3+. They explain why adding a ligand can dissolve an otherwise insoluble salt (silver chloride dissolves in ammonia as [Ag(NH3)2]+), why analytical tests work, and how metals are carried in blood and rivers. A neutral coordination entity such as [Ni(CO)4] is not called a complex ion because it has no charge, but it is still a complex.
Silver chloride is famously insoluble, yet it dissolves in ammonia solution. The reason is the complex ion [Ag(NH3)2]+: ammonia ligands wrap the silver into a soluble, charged package, pulling the equilibrium away from solid AgCl. The same trick is used in photography and in analytical separations.
Forming the complex ion [Ag(NH3)2]+ dissolves silver chloride that water alone cannot.
Computing the charge trips people up: it is the metal's oxidation state plus the sum of ligand charges, not just the metal's charge. Neutral ligands (water, ammonia, CO) add zero; anionic ligands (chloride, cyanide) each subtract one.