1
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
$$- {3 \over 5} - {1 \over 5}i$$
2
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
3
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
D
circle whose radius is $$\sqrt 2$$ .
4
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
If $$z = {{\sqrt 3 } \over 2} + {i \over 2}\left( {i = \sqrt { - 1} } \right)$$,

then (1 + iz + z5 + iz8)9 is equal to :
A
1
B
–1
C
0
D
(-1 + 2i)9
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