Question

Let $A,B,C$ be three sets of complex numbers as defined below:
$A=\{z:Im(z)\ge 1\}B=\{z:|z-2-i|=3\}C=\{z:Re((1-i)z)=\sqrt{2}\}$

$ii)$ Let $z$ be any point in $A\cap B\cap C$. Then, $|z+1-i{|}^2+|z-5-i{|}^2$ lies between

• A. $40$ and $44$
• B. $25$ and $29$
• C. $30$ and $34$
• D. $35$ and $39$

Answer 1

The correct option is D $35$ and $39$

The points $(-1,1)$ and $(5,1)$ are the extremities of a diameter of the given circle.
Hence, $|z+1-i{|}^2+|z-5-i{|}^2=6^2=36$