Complex Numbers 2 Question 28
29. 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: 29. False
Solution:
- $|z+1-i|^{2}+|z-5-i|^{2}$
$$ \begin{aligned} & =(x+1)^{2}+(y-1)^{2}+(x-5)^{2}+(y-1)^{2} \\ & =2\left(x^{2}+y^{2}-4 x-2 y\right)+28 \\ & =2(4)+28=36 \quad\left[\because x^{2}+y^{2}-4 x-2 y=4\right] \end{aligned} $$
