1
JEE Main 2014 (Offline)
+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)
2
JEE Main 2013 (Offline)
+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
$$\,\pi - \theta \,\,$$
3
AIEEE 2012
+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.
4
AIEEE 2011
+4
-1
Let $$\alpha \,,\beta$$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots on the line Re z = 1, then it is necessary that :
A
$$\beta \, \in ( - 1,0)$$
B
$$\left| {\beta \,} \right| = 1$$
C
$$\beta \, \in (1,\infty )$$
D
$$\beta \, \in (0,1)$$
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