If α and β are different complex numbers with |β| = 1, then find |(β -α)/(1 - α'β)|

Solution:

For any complex number z, z z' = |z|².

It is given that |β| = 1. 

Then

|β|² = ββ'  = 1

Now, |(β -α)/(1 - α'β)| = |(β -α)/(ββ' - α'β)|  [because 1 = ββ']

= |β - α| / |β| |β' - α'|

=  |β - α| / 1 |β' - α'| [because |β| = 1]

= |β - α| / | (β - α)' |

= 1 (because |z| = |z'|, for any complex number z)

Therefore, |(β -α)/(1 - α'β)| = 1

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 17

If α and β are different complex numbers with |β| = 1, then find |(β -α)/(1 - α'β)|

Summary:

If α and β are different complex numbers with |β| = 1 then |(β -α)/(1 - α'β)| = 1