(i) (2+\sqrt{3}i,\ 2-\sqrt{3}i)
[ \text{A.M.} = \dfrac{(2+\sqrt{3}i)+(2-\sqrt{3}i)}{2} = \dfrac{4}{2} = 2 ]
Answer: (2)
(ii) ((a+b)^2,\ (a-b)^2)
[ \text{A.M.} = \dfrac{(a+b)^2+(a-b)^2}{2} = \dfrac{2(a^2+b^2)}{2} = a^2+b^2 ]
Answer: (a^2+b^2)
[ \text{A.M.} = \dfrac{(2+\sqrt{3}i)+(2-\sqrt{3}i)}{2} = \dfrac{4}{2} = 2 ]
Answer: (2)
[ \text{A.M.} = \dfrac{(a+b)^2+(a-b)^2}{2} = \dfrac{2(a^2+b^2)}{2} = a^2+b^2 ]
Answer: (a^2+b^2)