1
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The number of points of intersection of

$$|z - (4 + 3i)| = 2$$ and $$|z| + |z - 4| = 6$$, z $$\in$$ C, is :

A
0
B
1
C
2
D
3
2
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

The area of the polygon, whose vertices are the non-real roots of the equation $$\overline z = i{z^2}$$ is :

A
$${{3\sqrt 3 } \over 4}$$
B
$${{3\sqrt 3 } \over 2}$$
C
$${3 \over 2}$$
D
$${3 \over 4}$$
3
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1

Let $$A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}$$ and $$B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}$$. Then A $$\cap$$ B is :

A
a portion of a circle centred at $$\left( {0, - {1 \over {\sqrt 3 }}} \right)$$ that lies in the second and third quadrants only
B
a portion of a circle centred at $$\left( {0, - {1 \over {\sqrt 3 }}} \right)$$ that lies in the second quadrant only
C
an empty
D
a portion of a circle of radius $${2 \over {\sqrt 3 }}$$ that lies in the third quadrant only
4
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Let z1 and z2 be two complex numbers such that $${\overline z _1} = i{\overline z _2}$$ and $$\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi$$. Then :

A
$$\arg {z_2} = {\pi \over 4}$$
B
$$\arg {z_2} = - {{3\pi } \over 4}$$
C
$$\arg {z_1} = {\pi \over 4}$$
D
$$\arg {z_1} = - {{3\pi } \over 4}$$
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