1
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = $${\pi \over 2}$$ , then :
A
$$z\overline w = {{1 - i} \over {\sqrt 2 }}$$
B
$$\overline z w = i$$
C
$$z\overline w = {{ - 1 + i} \over {\sqrt 2 }}$$
D
$$\overline z w = -i$$
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If a > 0 and z = $${{{{\left( {1 + i} \right)}^2}} \over {a - i}}$$, has magnitude $$\sqrt {{2 \over 5}}$$, then $$\overline z$$ is equal to :
A
$$- {1 \over 5} + {3 \over 5}i$$
B
$$- {1 \over 5} - {3 \over 5}i$$
C
$${1 \over 5} - {3 \over 5}i$$
D
$$- {3 \over 5} - {1 \over 5}i$$
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
Let z $$\in$$ C be such that |z| < 1.

If $$\omega = {{5 + 3z} \over {5(1 - z)}}$$z, then :
A
4Im( $$\omega$$) > 5
B
5Im( $$\omega$$) < 1
C
5Re( $$\omega$$) > 4
D
5Re( $$\omega$$) > 1
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
All the points in the set
$$S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )$$ lie on a :
A
straight line whose slope is –1
B
straight line whose slope is 1.
C
circle whose radius is $$\sqrt 2$$ .