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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 49
Total: 52
If α and β are different complex numbers with |β| = 1, then find |
β−α
1−
−
α
β
|
Solution:  
We have , |
β−α
1−
−
α
β
|2 =
|β−α|2
|1−
−
α
β|2
=
(β−α)
––––––––
(β−α)
(1−
−
α
β)
––––––––––
(1−
−
α
β)
 =
(β−α)(
−
β
−
−
α
)
(1−
−
α
β)(1−α
−
β
)
 =
β
−
β
−β
−
α
−α
−
β
+α
−
α
1−α
−
β
−
−
α
β+α
−
α
β
−
β
=
1−
−
α
β−α
−
β
+α
−
α
1−
−
α
β−α
−
β
+
−
α
α
 = 1
∴ |
β−α
1−
−
α
β
|2 = 1 ⇒ |
β−α
1−
−
α
β
| = 1
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