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:
- $|z+1-i|^{2}+|z-5-i|^{2}$
$ \begin{alignedat} & =(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} $
BETA
