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4-1.Complex numbers
medium
જો $(a + ib)(c + id)(e + if)(g + ih)$$ = A + iB,$ તો $({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2})$ =
A
${A^2} + {B^2}$
B
${A^2} - {B^2}$
C
${A^2}$
D
${B^2}$
Solution
(a)$(a + ib)(c + id)(e + if)(g + ih) = A + iB$…..$(i)$
==> $(a – ib)(c – id)(e – if)(g – ih) = A – iB$……$(ii)$
Multiplying $ (i) $ and $(ii),$ we get
$({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2}) = {A^2} + {B^2}$
Standard 11
Mathematics
