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If α , β are two different complex numbers such that | α | = 1, | β | = 1, then the expression | β − α /1 − α β | equals
  • a)
    1/2
  • b)
    1
  • c)
    2
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If α , β are two different complex numbers such that | &alp...
Solution:
To find the value of the expression | β - α / (1 - α β) |, we first need to simplify the expression inside the modulus.

Step 1: Simplify the expression inside the modulus
Given: | α | = 1, | β | = 1
We know that for any complex number z, | z | = 1 represents z lies on the unit circle in the complex plane.
So, both α and β lie on the unit circle.
Now, let's simplify the expression:
β - α / (1 - α β)
= β - α / (1 - αβ) / (1 - αβ)
= β - α / 1 - αβ
= (β - α) / (1 - αβ)

Step 2: Find the modulus of the expression
Now, we need to find the modulus of the expression (β - α) / (1 - αβ)
| (β - α) / (1 - αβ) |
= | β - α | / | 1 - αβ |
= | β - α | / | 1 - α|| β |
Since | α | = 1 and | β | = 1, the modulus of both α and β is 1.
Therefore, | (β - α) / (1 - αβ) | = | β - α | / | 1 - αβ |
= 1 / | 1 - αβ |
= 1
Therefore, the expression | β - α / (1 - α β) | equals 1. So, the correct answer is option 'b'.
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If α , β are two different complex numbers such that | α | = 1, | β | = 1, then the expression | β − α /1 − α β | equalsa)1/2b)1c)2d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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