1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
If z is a complex number such that $${{z - i} \over {z - 1}}$$ is purely imaginary, then the minimum value of | z $$-$$ (3 + 3i) | is :
A
$$2\sqrt 2 - 1$$
B
$$3\sqrt 2$$
C
$$6\sqrt 2$$
D
$$2\sqrt 2$$
2
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :
A
S contains exactly two elements
B
S contains only one element
C
S is a circle in the complex plane
D
S is a straight line in the complex plane
3
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
If $${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$$, then p and q are roots of the equation :
A
$${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
B
$${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
C
$${x^2} + \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$
D
$${x^2} - \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$
4
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The equation $$\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$$ represents a circle with :
A
centre at (0, $$-$$1) and radius $$\sqrt 2$$
B
centre at (0, 1) and radius $$\sqrt 2$$
C
centre (0, 0) and radius $$\sqrt 2$$
D
centre at (0, 1) and radius 2
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