1
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
If z and $$\omega$$ are two complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$\arg (z) - \arg (\omega ) = {{3\pi } \over 2}$$, then $$\arg \left( {{{1 - 2\overline z \omega } \over {1 + 3\overline z \omega }}} \right)$$ is :

(Here arg(z) denotes the principal argument of complex number z)
A
$${\pi \over 4}$$
B
$$- {{3\pi } \over 4}$$
C
$$- {\pi \over 4}$$
D
$${{3\pi } \over 4}$$
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let a complex number be w = 1 $$-$$ $${\sqrt 3 }$$i. Let another complex number z be such that |zw| = 1 and arg(z) $$-$$ arg(w) = $${\pi \over 2}$$. Then the area of the triangle with vertices origin, z and w is equal to :
A
4
B
$${1 \over 4}$$
C
2
D
$${1 \over 2}$$
3
JEE Main 2021 (Online) 18th March Morning Shift
+4
-1
If the equation $$a|z{|^2} + \overline {\overline \alpha z + \alpha \overline z } + d = 0$$ represents a circle where a, d are real constants then which of the following condition is correct?
A
|$$\alpha$$|2 $$-$$ ad $$\ne$$ 0
B
|$$\alpha$$|2 $$-$$ ad > 0 and a$$\in$$R $$-$$ {0}
C
|$$\alpha$$|2 $$-$$ ad $$\ge$$ 0 and a$$\in$$R
D
$$\alpha$$ = 0, a, d$$\in$$R+
4
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
Let S1, S2 and S3 be three sets defined as

S1 = {z$$\in$$C : |z $$-$$ 1| $$\le$$ $$\sqrt 2$$}

S2 = {z$$\in$$C : Re((1 $$-$$ i)z) $$\ge$$ 1}

S3 = {z$$\in$$C : Im(z) $$\le$$ 1}

Then the set S1 $$\cap$$ S2 $$\cap$$ S3 :
A
has exactly three elements
B
is a singleton
C
has infinitely many elements
D
has exactly two elements
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