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Question

If α and β are two different complex numbers with |β|=1, then βα1¯αβ is equal to.

A
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B
1
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C
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D
1
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Solution

The correct option is B 1
Let t=βα1¯¯¯¯αβ
Multiply the numerator and denominator with ¯¯¯β
t=∣ ∣1α¯¯¯β¯¯¯β¯¯¯¯α∣ ∣=∣ ∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯1α¯¯¯β¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯β¯¯¯¯α∣ ∣=1¯¯¯¯αββα=1t
t2=1
t=1

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