If 1 + i α 1 − i α = A + i B , then A 2 + B 2 equals to

A + i B = 1 + i α 1 − i α ⇒ A − i B = 1 − i α 1 + i α ⇒ ( A + i B ) ( A − i B ) = ( 1 + i α ) ( 1 − i α ) ( 1 − i α ) ( 1 + i α ) = 1 ⇒ A 2 + B 2 = 1

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MathematicsPermutation & CombinationnPr & nCrMedium2 minPYQ_2010

MathematicsMediumsingle choice

If $\frac{1 - i α}{1 + i α} = A + i B$ , then $A^{2} + B^{2}$ equals to

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Solution:

$A + i B = \frac{1 - i α}{1 + i α} \Rightarrow A - i B = \frac{1 + i α}{1 - i α} \Rightarrow (A + i B) (A - i B) = \frac{( 1 - i α ) ( 1 + i α )}{( 1 + i α ) ( 1 - i α )} = 1 \Rightarrow A^{2} + B^{2} = 1$

Stream:BITSATSubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: PYQ_2010

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