SATHEE: Complex Numbers 2 Question 28

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

(d) 40 and 44

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Answer:

Correct Answer: 29. (c)

Solution:

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

$\begin{aligned} = (x + 1)^{2} + (y - 1)^{2} + (x - 5)^{2} + (y - 1)^{2} \\ = 2 (x^{2} + y^{2} - 4 x - 2 y) + 28 \\ = 2 (4) + 28 = 36 [∵ x^{2} + y^{2} - 4 x - 2 y = 4] \end{aligned}$

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Complex Numbers 2 Question 28

29.

Answer:

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