Let A = z ∈ C : 1 ⩽ z - 1 + i ⩽ 2 and B = z ∈ A : z - 1 - i = 1 . Then, B

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MathematicsComplex NumberGeometric ApplicationEasy2 minPYQ_2022

MathematicsEasysingle choice

Let $A = \{z \in C : 1 ⩽ |z - (1 + i)| ⩽ 2\}$ and $B = \{z \in A : |z - (1 - i)| = 1\}$ . Then, $B$

Answer:

Solution:

$|z - (1 + i)| = 1 & |z - (1 + i)| = 2$ represents two concentric circles with centre $(1, 1)$ .

$|z - (1 - i)| = 1$ represents a circle with centre $(1, - 1)$ and radius $1$

$A$ represents the region between the concentric circles with centre $(1, 1)$

Set $B$ contains all points on minor arc $P Q$ of the circle $|z - (1 - i)| = 1$ .

Hence, $B$ has infinite elements.

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Geometric Application

⏱ 2mℹ️ Source: PYQ_2022

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