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1
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let C be the set of all complex numbers. Let

S1 = {z$$\in$$C : |z $$-$$ 2| $$\le$$ 1} and

S2 = {z$$\in$$C : z(1 + i) + $$\overline z$$(1 $$-$$ i) $$\ge$$ 4}.

Then, the maximum value of $${\left| {z - {5 \over 2}} \right|^2}$$ for z$$\in$$S1 $$\cap$$ S2 is equal to :
A
$${{3 + 2\sqrt 2 } \over 4}$$
B
$${{5 + 2\sqrt 2 } \over 2}$$
C
$${{3 + 2\sqrt 2 } \over 2}$$
D
$${{5 + 2\sqrt 2 } \over 4}$$
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Let C be the set of all complex numbers. Let

$${S_1} = \{ z \in C||z - 3 - 2i{|^2} = 8\}$$

$${S_2} = \{ z \in C|{\mathop{\rm Re}\nolimits} (z) \ge 5\}$$ and

$${S_3} = \{ z \in C||z - \overline z | \ge 8\}$$.

Then the number of elements in $${S_1} \cap {S_2} \cap {S_3}$$ is equal to :
A
1
B
0
C
2
D
Infinite
3
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let n denote the number of solutions of the equation z2 + 3$$\overline z$$ = 0, where z is a complex number. Then the value of $$\sum\limits_{k = 0}^\infty {{1 \over {{n^k}}}}$$ is equal to
A
1
B
$${4 \over 3}$$
C
$${3 \over 2}$$
D
2
4
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
If z and $$\omega$$ are two complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$\arg (z) - \arg (\omega ) = {{3\pi } \over 2}$$, then $$\arg \left( {{{1 - 2\overline z \omega } \over {1 + 3\overline z \omega }}} \right)$$ is :

(Here arg(z) denotes the principal argument of complex number z)
A
$${\pi \over 4}$$
B
$$- {{3\pi } \over 4}$$
C
$$- {\pi \over 4}$$
D
$${{3\pi } \over 4}$$
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