Complex Numbers Ques 32
Let $z$ be any point in $A \cap B \cap C$ and let $w$ be any point satisfying $|w-2-i|<3$. Then, $|z|-|w|+3$ lies between
(a) $-6$ and $3$
(b) $-3$ and $6$
(c) $-6$ and $6$
(d) $-3$ and $9$
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Answer:
Correct Answer: 32.(d)
Solution:
Formula:
- Since,
$ |w-(2+i)|<3 \Rightarrow|w|-|2+i|<3 $
$ \begin{array}{ll} \Rightarrow & -3+\sqrt{5}<|w|<3+\sqrt{5} \\ \Rightarrow & -3-\sqrt{5}<-|w|<3-\sqrt{5} \end{array} $
Also, $\quad|z-(2+i)|=3$
$ \begin{array}{ll} \Rightarrow & -3+\sqrt{5} \leq|z| \leq 3+\sqrt{5} \\ \therefore & -3<|z|-|w|+3<9 \end{array} $
BETA
