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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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Given, `|beta|=1`
`implies" "betabar(beta)=1" or "beta=(1)/(beta)" "(1)`
Now, `|(beta-alpha)/(1-bar(alpha)beta)|=|((1)/(bar(beta))-alpha)/(1-bar(alpha)beta)|=|(1)/(bar(beta))||(1-alphabar(beta))/(1-bar(alpha)beta)|=(1)/(|beta|)|bar(1-alphabar(beta))/(1-bar(alpha)beta)|`
`=|(1-bar(alpha)beta)/(1-bar(alpha)beta)|=1`
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