1.

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`

Answer» `(a+ib)(c+id)(e+if)(g+ih)=(A+iB)`
`rArr" "|(a+ib)(c+id)(e+if)(g+ih)=|A+iB|`
`rArr" "|a+ib|*|"c+id"|*|"e+if"|*|g+ih|=|A+iB|`
`rArr" "|a+ib|^(2)*|"c+id"|^(2)*|"e+if"|^(2)*|g+ih|^(2)=|A+iB|^(2)`
`rArr" "(a^(2)+b^(2))(c^(2)+d^(2))(e^(2)+f^(2))(g^(2)+h^(2))=(A^(2)+B^(2))`.
Hence, `(a^(2)+b^(2))(c^(2)+d^(2))(e^(2)+f^(2))(g^(2)+h^(2))=(A^(2)+B^(2))`.


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