1
JEE Main 2022 (Online) 29th June Morning Shift
Numerical
+4
-1

Let $$S = \{ z \in C:|z - 2| \le 1,\,z(1 + i) + \overline z (1 - i) \le 2\}$$. Let $$|z - 4i|$$ attains minimum and maximum values, respectively, at z1 $$\in$$ S and z2 $$\in$$ S. If $$5(|{z_1}{|^2} + |{z_2}{|^2}) = \alpha + \beta \sqrt 5$$, where $$\alpha$$ and $$\beta$$ are integers, then the value of $$\alpha$$ + $$\beta$$ is equal to ___________.

2
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1

Sum of squares of modulus of all the complex numbers z satisfying $$\overline z = i{z^2} + {z^2} - z$$ is equal to ___________.

3
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1

The number of elements in the set {z = a + ib $$\in$$ C : a, b $$\in$$ Z and 1 < | z $$-$$ 3 + 2i | < 4} is __________.

4
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1

If $${z^2} + z + 1 = 0$$, $$z \in C$$, then

$$\left| {\sum\limits_{n = 1}^{15} {{{\left( {{z^n} + {{( - 1)}^n}{1 \over {{z^n}}}} \right)}^2}} } \right|$$ is equal to _________.

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