यदि `alpha` और `beta` भिन्न-भिन्न सम्मिश्र संख्याऍं हैं, जहाँ`|alpha|=1` है, तो `|(alpha-beta)/(1-alpha beta)|` किसके बराबर है ?

Options

A. `|beta|`
B. 2
C. 1
D. 0

Answer

C

Explanation

`|(alpha-beta)/(1-alphabeta)| = |(alpha-beta)/(alphabaralpha- alphabeta)|`
` [:" |alpha|= 1 rArr |alpha|^(2) = 1 rArr alpha.baralpha= 1]`
` = |(alpha-beta)/(alpha(baralpha - barbeta))|`
` = 1/(|alpha|)|(alpha-beta)/(baralpha-barbeta)|`
` = (|alpha-beta|)/(|alpha||bar(alpha-beta)|)`
` = (|alpha-beta|)/(|alpha||alpha-beta|)" "[:'|barz|=|barz|]`
` = 1/(|alpha|)" "[:'|alpha| =1]`
= 1