1
JEE Main 2015 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
A complex number z is said to be unimodular if $$\,\left| z \right| = 1$$. Suppose $${z_1}$$ and $${z_2}$$ are complex numbers such that $${{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}$$ is unimodular and $${z_2}$$ is not unimodular. Then the point $${z_1}$$ lies on a :
A
circle of radius 2.
B
circle of radius $${\sqrt 2 }$$.
C
straight line parallel to x-axis
D
straight line parallel to y-axis.
2
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
If z is a complex number such that $$\,\left| z \right| \ge 2\,$$, then the minimum value of $$\,\,\left| {z + {1 \over 2}} \right|$$ :
A
is strictly greater that $${{5 \over 2}}$$
B
is strictly greater that $${{3 \over 2}}$$ but less than $${{5 \over 2}}$$
C
is equal to $${{5 \over 2}}$$
D
lie in the interval (1, 2)
3
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
If z is a complex number of unit modulus and argument $$\theta $$, then arg $$\left( {{{1 + z} \over {1 + \overline z }}} \right)$$ equals :
A
$$ - \theta \,\,$$
B
$${\pi \over 2} - \theta \,$$
C
$$\theta \,$$
D
$$\,\pi - \theta \,\,$$
4
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
If $$z \ne 1$$ and $$\,{{{z^2}} \over {z - 1}}\,$$ is real, then the point represented by the complex number z lies :
A
either on the real axis or a circle passing through the origin.
B
on a circle with centre at the origin
C
either on real axis or on a circle not passing through the origin.
D
on the imaginary axis.
JEE Main Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
CBSE
Class 12