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  • <img alt="\mathrm{Let\; A= \left \{ z\in C:1\leqslant \left | z-\left ( 1+i \right ) \right |\leqslant 2 \right \} }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BLet%5C%3B%20A%

\mathrm{Let\; A= \left \{ z\in C:1\leqslant \left | z-\left ( 1+i \right ) \right |\leqslant 2 \right \} }
\mathrm{and\; B= \left \{ z\in A:\left | z-\left ( 1-i \right ) \right |= 1 \right \} }. Then, B:

Option: 1

is an empty set


Option: 2

contains exactly two elements


Option: 3

contains exactly three elements


Option: 4

is an infinite set


Answers (1)

best_answer

\mathrm{A= \left \{ z\in C:1\leqslant \left | z-\left ( 1+i \right ) \right |\leqslant 2 \right \}}
\mathrm{ B= \left \{ z\in A:\left | z-\left ( 1-i \right ) \right |= 1 \right \} }
\mathrm{ A:1\leqslant \left ( x-1 \right )^{2}+\left ( y-1 \right )^{2} \leqslant 4}



Hence B is an infinite set. 
The correct answer is option (D)

Posted by

Sayak

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