1
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
If $${\mathop{\rm Re}\nolimits} \left( {{{z - 1} \over {2z + i}}} \right) = 1$$, where z = x + iy, then the point (x, y) lies on a :
A
straight line whose slope is $${3 \over 2}$$
B
straight line whose slope is $$-{2 \over 3}$$
C
circle whose diameter is $${{\sqrt 5 } \over 2}$$
D
circle whose centre is at $$\left( { - {1 \over 2}, - {3 \over 2}} \right)$$
2
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
Let z $$\in$$ C with Im(z) = 10 and it satisfies $${{2z - n} \over {2z + n}}$$ = 2i - 1 for some natural number n. Then :
A
n = 20 and Re(z) = –10
B
n = 40 and Re(z) = 10
C
n = 40 and Re(z) = –10
D
n = 20 and Re(z) = 10
3
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
The equation |z – i| = |z – 1|, i = $$\sqrt { - 1}$$, represents :
A
B
the line through the origin with slope – 1
C
a circle of radius $${1 \over 2}$$
D
the line through the origin with slope 1
4
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = $${\pi \over 2}$$ , then :
A
$$z\overline w = {{1 - i} \over {\sqrt 2 }}$$
B
$$\overline z w = i$$
C
$$z\overline w = {{ - 1 + i} \over {\sqrt 2 }}$$
D
$$\overline z w = -i$$
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