Complex Numbers Ques 33

Passage II

Let $S=S _1 \cap S _2 \cap S _3$, where

$S _1=\{z \in C:|z|<4\}, S _2=z \in C: \operatorname{lm} [\frac{z-1+\sqrt{3} i}{1-\sqrt{3} i}]>0$

and $S _3:\{z \in C: \operatorname{Re} z>0\}$

(2008)

Let $z$ be any point in $A \cap B \cap C$.

The $|z+1-i|^{2}+|z-5-i|^{2}$ lies between

(a) $25$ and $29$

(b) $30$ and $34$

(c) $35$ and $39$

(d) $40$ and $44$

Show Answer

Answer:

Correct Answer: 33.(c)

Solution:

Formula:

Equation of circle:

  1. $|z+1-i|^{2}+|z-5-i|^{2}$

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



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