If `(a" "+" "i b)" "(c" "+" "i d)" "(e" "+" "if)" "(g" "+" "i h)" "=" "A" "+" "i B` , then show that `(a^2+b^2)(c^2+d^2)(e^2+f^2)(g^2+h^2)=A^2+B^2`

(a+ib)(c+id)(e+if)(g+ih)=A+iB, then show that (a^(2)+b^(2))(c^(2)+d^(2))(e^(2)+f^(2))(g^(2)+h^(2))=A^(2)+B^(2)

If (a+ib)(c+id)(e+ if )(g+ih)=A+iB prove that (a^(2)+b^(2))(c^(2)+d^(2))(e^(2)+f^(2))(g^(2)+h^(2))=A^(2)+B^(2)

If a,b,c,d be in G.P. show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2.

If a,b,c,d………are in G.P., then show that (a+b)^2, (b+c)^2, (c+d)^2 are in G.P.

If a,b,c,d………are in G.P., then show that (a-b)^2, (b-c)^2, (c-d)^2 are in G.P.

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

If a,b,c are in HP,b,c,d are in GP and c,d,e are in AP, than show that e=(ab^(2))/(2a-b)^(2) .

If U" "=" "{a ," "b ," "c ," "d ," "e ," "f," "g," "h} , find the complements of the following sets : (i) A" "=" "{a ," "b ," "c} (ii) B" "=" "{d ," "e ," "f," "g] (iii) C" "=" "{a ," "c ," "e ," "g} (iv) D" "=" "{f," "g," "h ," "a)

If a, b, c , d are in G.P. , then shown that (i) (a + b)^(2) , (b +c)^(2), (c + d)^(2) are in G.P. (ii) (1)/(a^(2) + b^(2)), (1)/(b^(2) +c^(2)), (1)/(c^(2) + a^(2)) are in G.P.