1
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
If $${{z - \alpha } \over {z + \alpha }}\left( {\alpha \in R} \right)$$ is a purely imaginary number and | z | = 2, then a value of $$\alpha$$ is :
A
$${1 \over 2}$$
B
$$\sqrt 2$$
C
2
D
1
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let z be a complex number such that |z| + z = 3 + i (where i = $$\sqrt { - 1}$$). Then |z| is equal to :
A
$${{\sqrt {34} } \over 3}$$
B
$${5 \over 3}$$
C
$${5 \over 4}$$
D
$${{\sqrt {41} } \over 4}$$
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Let $${\left( { - 2 - {1 \over 3}i} \right)^3} = {{x + iy} \over {27}}\left( {i = \sqrt { - 1} } \right),\,\,$$ where x and y are real numbers, then y $$-$$ x equals :
A
$$-$$ 85
B
85
C
$$-$$ 91
D
91
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5}.$$ If R(z) and 1(z) respectively denote the real and imaginary parts of z, then :
A
R(z) = $$-$$ 3
B
R(z) < 0 and I(z) > 0
C
I(z) = 0
D
R(z) > 0 and I(z) > 0
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