Let , , and be three sets of complex numbers defined below: A= z: Im (z) 1 B=…

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

A

B

, and

C

be three sets of complex numbers defined below:

A=\{z:\operatorname{Im}(z)\geq1\}

B=\{z:|z-2-i|=3\}

C=\left\{z:\operatorname{Re}((1-i)z)=\sqrt{2}\right\},\quad \text{where } i=\sqrt{-1}

Let

z

be any point in

A\cap B\cap C

and

\omega

be any point satisfying

|\omega-2-i|<3

. Then

|z|-|\omega|+3

lies between (1)

-6

and

3

(2)

-3

and

6

(3)

-6

and

6

(4)

-3

and

9