1
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
$${3 \over 4}$$
2
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
3
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
$$\arg {z_1} = - {{3\pi } \over 4}$$
4
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Let a circle C in complex plane pass through the points $${z_1} = 3 + 4i$$, $${z_2} = 4 + 3i$$ and $${z_3} = 5i$$. If $$z( \ne {z_1})$$ is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then $$arg(z)$$ is equal to:

A
$${\tan ^{ - 1}}\left( {{2 \over {\sqrt 5 }}} \right) - \pi$$
B
$${\tan ^{ - 1}}\left( {{{24} \over 7}} \right) - \pi$$
C
$${\tan ^{ - 1}}\left( 3 \right) - \pi$$
D
$${\tan ^{ - 1}}\left( {{3 \over 4}} \right) - \pi$$
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