These are four things to proving a set is a group - closure - associativity - existance of an identity - existance of an inverse for each element. Show closure: let z=a+bi and w = c+di be elements of the group C* then z*w = (a+bi)(c+di) = ....... Foil and simplify.... if your answer is in the form a+bi... then it proves that the group closed Prove associativity: let z=a+bi and w = c+di and y = e+fi be elements of the group C* (z*w)*y = z*(w*y)... foil and simplify... show that both sides will yield the same result -- work inside parenthesis first... Prove existance of an identity element.... Let e be the identity element in C* such that e*z=z Find e..... I am guessing that it is 1. Prove the existance of an inverse for each element of C*. Let z=a+bi and z\' be the inverse of z find z\' such that z*z\' = the identity (which as I said above - I think is 1) If you go through these four steps and they all work out - you have a group B) To be a subgroup... the set has to be a subset of C* and a group all on its own.. H is definately a subset of C*... you just have to show that it is a group (go through the 4 steps) Solution These are four things to proving a set is a group - closure - associativity - existance of an identity - existance of an inverse for each element. Show closure: let z=a+bi and w = c+di be elements of the group C* then z*w = (a+bi)(c+di) = ....... Foil and simplify.... if your answer is in the form a+bi... then it proves that the group closed Prove associativity: let z=a+bi and w = c+di and y = e+fi be elements of the group C* (z*w)*y = z*(w*y)... foil and simplify... show that both sides will yield the same result -- work inside parenthesis first... Prove existance of an identity element.... Let e be the identity element in C* such that e*z=z Find e..... I am guessing that it is 1. Prove the existance of an inverse for each element of C*. Let z=a+bi and z\' be the inverse of z find z\' such that z*z\' = the identity (which as I said above - I think is 1) If you go through these four steps and they all work out - you have a group B) To be a subgroup... the set has to be a subset of C* and a group all on its own.. H is definately a subset of C*... you just have to show that it is a group (go through the 4 steps).