1
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
If the four complex numbers $$z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)$$ and $$z-2Re(z)$$ represent the vertices of a square of side 4 units in the Argand plane, then $$|z|$$ is equal to :
A
4$$\sqrt 2$$
B
4
C
2
D
2$$\sqrt 2$$
2
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
If a and b are real numbers such that
$${\left( {2 + \alpha } \right)^4} = a + b\alpha$$
where $$\alpha = {{ - 1 + i\sqrt 3 } \over 2}$$ then a + b is equal to :
A
33
B
9
C
24
D
57
3
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $$u = {{2z + i} \over {z - ki}}$$, z = x + iy and k > 0. If the curve represented
by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :
A
2
B
4
C
1/2
D
3/2
4
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
If z1 , z2 are complex numbers such that
Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and
arg(z1 - z2) = $${\pi \over 6}$$, then Im(z1 + z2 ) is equal to :
A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over {\sqrt 3 }}$$
C
$${2 \over {\sqrt 3 }}$$
D
$${2\sqrt 3 }$$
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