1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
The set of all $$\alpha$$ $$\in$$ R, for which w = $${{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}$$ is purely imaginary number, for all z $$\in$$ C satisfying |z| = 1 and Re z $$\ne$$ 1, is :
A
an empty set
B
{0}
C
$$\left\{ {0,{1 \over 4}, - {1 \over 4}} \right\}$$
D
equal to R
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
The equation
Im $$\left( {{{iz - 2} \over {z - i}}} \right)$$ + 1 = 0, z $$\in$$ C, z $$\ne$$ i
represents a part of a circle having radius equal to :
A
2
B
1
C
$${3 \over 4}$$
D
$${1 \over 2}$$
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Let z$$\in$$C, the set of complex numbers. Then the equation, 2|z + 3i| $$-$$ |z $$-$$ i| = 0 represents :
A
a circle with radius $${8 \over 3}.$$
B
a circle with diameter $${{10} \over 3}.$$
C
an ellipse with length of major axis $${{16} \over 3}.$$
D
an ellipse with length of minor axis $${{16} \over 9}.$$
4
JEE Main 2017 (Offline)
+4
-1
Let $$\omega$$ be a complex number such that 2$$\omega$$ + 1 = z where z = $$\sqrt {-3}$$. If

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$,

then k is equal to :
A
z
B
-1
C
1
D
-z
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