'Desu' is normally the 'copula'. And 'imasu' (from iru) is used to denote the physical existence of living things, and to make -te form in a Present Progressive. Like: Neko desu -> It's a/the cat. Neko ga imasu -> There is a/the cat. Asoko ni neko ga imasu -> There goes a cat. Denwa de hanashite imasu. -> I’m talking on the phone. 'Desu' is not always conjugated, and sometimes just added to raise the politenesslevel of a sentence: Kono hon wa tanoshii (desu) -> This is a fun book. Kono hon wa tanoshikunai (desu) This book is no fun. Onaka ga itai (desu) -> My stomach hurts. Atarashii kuruma ga hoshii (desu) -> I want a new car. So, "toshi wo totte imasu" -> "I am old." (Or "I have become old") toru = to be old; -te form: totte imasu futoru = to get fat, to put on weight; -te form: "futotte imasu" -> "I am fat" (Or "I have become fat") te + iru in these expressions does NOT mean: "is becoming," but either "has become" or "is in that state". So, in your case, imasu is just part of forming a Present Progressive in idioms with a special meaning. And the occurances of 'desu' are just put after the I-adjective (takai = tall) for politeness, or as verb (after kanemochi = rich man).