1
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
Let a complex number z, |z| $$\ne$$ 1,

satisfy $${\log _{{1 \over {\sqrt 2 }}}}\left( {{{|z| + 11} \over {{{(|z| - 1)}^2}}}} \right) \le 2$$. Then, the largest value of |z| is equal to ____________.
A
5
B
8
C
6
D
7
2
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If $$\alpha$$, $$\beta$$ $$\in$$ R are such that 1 $$-$$ 2i (here i2 = $$-$$1) is a root of z2 + $$\alpha$$z + $$\beta$$ = 0, then ($$\alpha$$ $$-$$ $$\beta$$) is equal to :
A
$$-$$7
B
7
C
3
D
$$-$$3
3
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
Let the lines (2 $$-$$ i)z = (2 + i)$$\overline z$$ and (2 $$+$$ i)z + (i $$-$$ 2)$$\overline z$$ $$-$$ 4i = 0, (here i2 = $$-$$1) be normal to a circle C. If the line iz + $$\overline z$$ + 1 + i = 0 is tangent to this circle C, then its radius is :
A
$${3 \over {2\sqrt 2 }}$$
B
$$3\sqrt 2$$
C
$${1 \over {2\sqrt 2 }}$$
D
$${3 \over {\sqrt 2 }}$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Let z = x + iy be a non-zero complex number such that $${z^2} = i{\left| z \right|^2}$$, where i = $$\sqrt { - 1}$$ , then z lies on the :
A
line, y = –x
B
real axis
C
line, y = x
D
imaginary axis
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