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Flag Algebra> Sir please tell me question no 1. I'm not...
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Sir please tell me question no 1.I'm not getting the answer.Its answer is (b).

Pushkar Kumar , 5 Years ago
Grade 12
anser 1 Answers
Samyak Jain

Last Activity: 5 Years ago

Given : (1 – ix) / (1 + ix) = a – ib , a2 + b2 = 1,  a,b \epsilon R.
Solution : (1 – ix) / (1 + ix)  =  [ (1 – ix) / (1 + ix) ] [(1 – ix) / (1 – ix)]  =  (1 – ix)2 / (1 – i2x2)
   =  (1 – 2ix + i2x2) / (1 + x2)  =  (1 – x2 – 2ix) / (1 + x2)      [\because i2 = – 1]
  =  (1 – x2) / (1 + x2)  –  i2x / (1 + x2)  =  a – ib
 
\therefore a = (1 – x2) / (1 + x2)    ...(1)  &  b = 2x / (1 + x2)   ...(2)
Add 1 on both sides of (1).
\Rightarrow a + 1 = 2 / (1 + x2)           ...(3)
Divide (2) by (3).
\Rightarrow b / (a + 1)  =  x  i.e.  x  =  2b / 2(a + 1) = 2b / (2a + 1 + 1)
x  =  2b / (2a + 1 + a2 + b2)  \Rightarrow x =  2b / { (1 + a)2 + b2 }

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