Let A = \{ z C : 1 ≤ |z-(1+i)| ≤ 2 \} and B = \{ z A : |z-(1-i)| = 1 \}. Then, B : [24-Jun-2022-Shift-1]

Correct Answer is : is an infinite set

contains exactly three elements

Correct Answer is : is an infinite set

Test Index

Complex Numbers Part 1

Section: Mathematics

Question : 6 of 100

Marks: +1, -0

Let

A = \{ z \in C : 1 \le |z-(1+i)| \le 2 \}

B = \{ z \in A : |z-(1-i)| = 1 \}

B

Solution: 👈: Video Solution

Let,

z = x + i y

Given,

1 \le |z-(1+i)| \le 2

\Rightarrow 1 \le |x + i y - 1 - i| \le 2

\Rightarrow 1 \le |(x-1) + i(y-1)| \le 2

\Rightarrow 1 \le \sqrt{(x-1)^2 + (y-1)^2} \le 2

It represent two concentric circle both have center at

(1,1)

and radius 1 and 2 .

Also given,

|z-(1-i)| = 1

\Rightarrow |x + i y - 1 + i| = 1

\Rightarrow |(x-1) + i(y+1)| = 1

\Rightarrow \sqrt{(x-1)^2 + (y+1)^2} = 1

This represent a circle with center at

=1

and radius

=1

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