option (i) iam not sure but let r = (a+b)
L(a+b)* = { Ɛ ,a ,b, ab, ba ,abb ,.......} = LHS
RHS = ( L(R) ) * = ( a+b)* there fore LHS = RHS it holds
(ii) $(a^+ + \phi ^*)^* = (a^+ + \phi )^*$
= $(a^+ + \epsilon )^* = ( a^+)^*$
=$(a^*)^* = (a)^*$
hence it holds
(iii) $(a^+)^* = (a^*)^+$
holds always as $(R^*)^+ = (R^+)^*$
(iv) $(a^+ + \phi^* )^+ = (a^+ + \phi )^*$
$(\epsilon +a^+)^+ = (a^+)^*$
$(a^*)^+ = (a^+)^*$
hold true
Therefore , All options correct
remember $\phi + R = R$
and $\epsilon + R^+ = R^*$