1
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
The value of $${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ is :
A
–215i
B
–215
C
215i
D
65
2
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$$\sqrt 2$$
3
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
4
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
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