1
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 ___________.

2
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 __________.

3
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 _________.

4
JEE Main 2022 (Online) 24th June Evening Shift
Numerical
+4
-1

Let S = {z $$\in$$ C : |z $$-$$ 3| $$\le$$ 1 and z(4 + 3i) + $$\overline z$$(4 $$-$$ 3i) $$\le$$ 24}. If $$\alpha$$ + i$$\beta$$ is the point in S which is closest to 4i, then 25($$\alpha$$ + $$\beta$$) is equal to ___________.

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