1
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
2
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
3
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let z1 and z2 be any two non-zero complex numbers such that   $$3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|.$$  If  $$z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}}$$  then -
A
$${\rm I}m\left( z \right) = 0$$
B
$$\left| z \right| = \sqrt {{17 \over 2}}$$
C
$$\left| z \right| =$$ $${1 \over 2}\sqrt {9 + 16{{\cos }^2}\theta }$$
D
Re(z) $$=$$ 0
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz$$_0^{81}$$ $$-$$ 3iz$$_0^{93}$$, then arg z is equal to :
A
$${\pi \over 4}$$
B
$${\pi \over 6}$$
C
$${\pi \over 3}$$
D
0
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