MCQ
$\begin{array}{l}\text { If }(a+i b)(c+i d)(e+i f)(g+i h)=A+i B \text {, then } \\ \left(a^2+b^2\right)\left(c^2+d^2\right)\left(e^2+f^2\right)\left(g^2+h^2\right)=\end{array}$
  • $A^2+B^2$
  • B
    $A^2-B^2$
  • C
    $A ^2$
  • D
    $B ^2$

Answer

Correct option: A.
$A^2+B^2$
(A)
$(a+i b)(c+i d)(e+i f)(g+i h)=A+i B$ ...(i)
$\Rightarrow( a - ib )( c - id )( e - if )( g - ih )= A - iB$ ...(ii)
Multiplying (i) and (ii), we get
$\left( a ^2+ b ^2\right)\left( c ^2+ d ^2\right)\left( e ^2+ f ^2\right)\left( g ^2+ h ^2\right)= A ^2+ B ^2$

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