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If `az^(2)+bz+1=0` where `a,b, in C` and `|a|=(1)/(2)` have a root `alpha` such that `|alpha|=1` then `4|avecb-b|` is equal to |
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Answer» Correct Answer - 3 `aalpha^(2)+balpha+1=0` `impliesb=-(1)/(alpha)-aalpha` `b=-overline(alpha)-aalpha` `overline(b)=-alpha-overline(a)overline(alpha)` `aoverline(b)=-aalpha-|overline(a)|^(2)overline(alpha)` `=-aalpha-(1)/(4)overline(alpha)` `aoverline(b)-b=-aalpha-(1)/(4)overline(alpha),overline(alpha)+aalpha=(3)/(4)overlie(alpha)` `|aoverline(b)-b|=(3)/(4)|overline(alpha)|=(3)/(4)` |
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