Paragraph: Let $A, B, C$ be three sets of complex numbers as defined below. $A=\{z ; \operatorname{lm} z \geq 1\} ; B=\{z:|z-2-i|=3\} ; C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\}$. Question: Let $z$ be any point in $A \cap B \cap C$. The $|z+1-i|^2+|z-5-i|^2$ lies between

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Aicharya · Accepted Answer

$|z+1-i|^2+|z-5-i|^2=(x+1)^2+(y-1)^2+(x-5)^2+(y-1)^2$ $ \begin{aligned} & =2\left(x^2+y^2-4 x-2 yight)+28 \ & =2(4)+28 \ & {\left[\because x^2+y^2-4 x-2 y=4ight]} \ & =36 \ & \end{aligned} $

Paragraph: Let $A, B, C$ be three sets of complex numbers as defined below. $A=\{z ; \operatorname{lm} z…

Solution