MCQ
If $(a + ib)(c + id)(e + if)(g + ih)$$ = A + iB,$ then $({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2})$ =
- ✓${A^2} + {B^2}$
- B${A^2} - {B^2}$
- C${A^2}$
- D${B^2}$
✓
Answer
Correct option: A.
${A^2} + {B^2}$
a
(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
$({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2}) = {A^2} + {B^2}$
(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
$({a^2} + {b^2})({c^2} + {d^2})({e^2} + {f^2})({g^2} + {h^2}) = {A^2} + {B^2}$
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