Let A,B,C be three sets of complex number as defined below `A={z:lm (z) ge 1}` `B={z:|z-2-i|=3}` `C={z:Re((1-i)z)=sqrt(2)}` Let z be any point in `A cap B cap C` and let w be any point satisfying `|w-2-i|lt 3` Then `|z|-|w|+3` lies betweenA. `-6 and 3`B. `-3 and 6`C. `-6 and 6`D. `-3 and 9 `

Let A,B,C be three sets of complex number as defined below `A={z:lm (z

1.	Let A,B,C be three sets of complex number as defined below `A={z:lm (z) ge 1}` `B={z:\|z-2-i\|=3}` `C={z:Re((1-i)z)=sqrt(2)}` Let z be any point in `A cap B cap C` and let w be any point satisfying `\|w-2-i\|lt 3` Then `\|z\|-\|w\|+3` lies betweenA. `-6 and 3`B. `-3 and 6`C. `-6 and 6`D. `-3 and 9 `
Answer» Correct Answer - D Since `\|w-(2+i)\| lt 3 rArr \|w\|-\|2+i\|lt 3 ` `rArr -3+sqrt(5)lt \|w\| lt 3 + sqrt(5)` ltbr `rArr -3-sqrt(5)lt -\|w\|lt 3 -sqrt(5)` Also `\|z-2(2+i)\|=3` `rArr -3 + sqrt(5) le \|z\| le 3 +sqrt(5)` `therefore -3 lt \|z\| -\|w\|+3 lt 9 `

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Let A,B,C be three sets of complex number as defined below `A={z:lm (z) ge 1}` `B={z:|z-2-i|=3}` `C={z:Re((1-i)z)=sqrt(2)}` Let z be any point in `A cap B cap C` and let w be any point satisfying `|w-2-i|lt 3` Then `|z|-|w|+3` lies betweenA. `-6 and 3`B. `-3 and 6`C. `-6 and 6`D. `-3 and 9 `

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