1
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

The real part of the complex number $${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$$ is equal to :

A
$${{500} \over {13}}$$
B
$${{110} \over {13}}$$
C
$${{55} \over {6}}$$
D
$${{550} \over {13}}$$
2
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $$-$$ 1) $$-$$ arg(z + 1) = $${\pi \over 4}$$ intersect :

A
exactly at one point.
B
exactly at two points.
C
nowhere.
D
at infinitely many points.
3
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

Let $$\alpha$$ and $$\beta$$ be the roots of the equation x2 + (2i $$-$$ 1) = 0. Then, the value of |$$\alpha$$8 + $$\beta$$8| is equal to :

A
50
B
250
C
1250
D
1500
4
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

The number of points of intersection of

$$|z - (4 + 3i)| = 2$$ and $$|z| + |z - 4| = 6$$, z $$\in$$ C, is :

A
0
B
1
C
2
D
3
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