1
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
2
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
$${3 \over {\sqrt 2 }}$$
3
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
4
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
The region represented by
{z = x + iy $$\in$$ C : |z| – Re(z) $$\le$$ 1} is also given by the
inequality: {z = x + iy $$\in$$ C : |z| – Re(z) $$\le$$ 1}
A
y2 $$\le$$ $$2\left( {x + {1 \over 2}} \right)$$
B
y2 $$\le$$ $${x + {1 \over 2}}$$
C
y2 $$\ge$$ 2(x + 1)
D
y2 $$\ge$$ x + 1
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