1
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

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

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

A
is an empty set
B
contains exactly two elements
C
contains exactly three elements
D
is an infinite set
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
If z is a complex number such that $${{z - i} \over {z - 1}}$$ is purely imaginary, then the minimum value of | z $$-$$ (3 + 3i) | is :
A
$$2\sqrt 2 - 1$$
B
$$3\sqrt 2$$
C
$$6\sqrt 2$$
D
$$2\sqrt 2$$
3
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :
A
S contains exactly two elements
B
S contains only one element
C
S is a circle in the complex plane
D
S is a straight line in the complex plane
4
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
If $${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$$, then p and q are roots of the equation :
A
$${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
B
$${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
C
$${x^2} + \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
D
$${x^2} - \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
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