For show that the following pairs of regular expressions define the same language over the alphabet Σ = {a b} :

(i) ((a + bb)*aa)* and Λ + (a + bb)*aa
(ii) (aa)*(A + a) and a*
(iii) a(aa)*(A + a)b + b and a*b
(iv) a(ba + a)*b and aa*b(aa*b)*
(v) Λ + a(a + b)* + (a + b)*aa(a + b)* and ((b*a)*ab*)*