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If alphaand betaare different complex n...

If `alpha`and `beta`are different complex numbers with `|beta|=1,`then find `|(beta-alpha)/(1- baralphabeta)|`.

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`|(beta-alpha)/(1-bar(alpha)beta)|^(2)=(( beta-alpha)/(1-bar(alpha)beta)) *bar(((beta-alpha)/(1-baralphabeta)))`
`=((beta-alpha)(bar(beta)-baralpha))/(( 1- bar alphabeta)(1-alphabarbeta))=(betabarbeta+alphabaralpha-alphabarbeta-baralpha beta )/(1+ alphabaralphabetabarbeta-alphabarbeta-baralphabeta)`
`" "=(|beta|^(2) + |alpha|^(2)-alphabarbeta-baralphabeta)/(1+|alpha|^(2)|beta|^(2)-alphabarbeta-baralphabeta)`
` " "=(1+|alpha|^(2)-alphabarbeta-baralphabeta)/(1+|alpha|^(2) -alphabarbeta-bar alphabeta)=1`
`rArr" "|(beta-alpha)/(1-baralphabeta)|=1`
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