1
IIT-JEE 2012 Paper 1 Offline
+4
-1
Let z be a complex number such that the imaginary part of z is non-zero and $$a\, = \,{z^2} + \,z\, + 1$$ is real. Then a cannot take the value
A
- 1
B
$${1 \over 3}$$
C
$${1 \over 2}$$
D
$${3 \over 4}$$
2
IIT-JEE 2010 Paper 2 Offline
+4
-1
Match the statements in Column I with those in Column II.

[Note : Here z takes value in the complex plane and Im z and Re z denotes, respectively, the imaginary part and the real part of z.]

Column I

(A) The set of points z satisfying $$\left| {z - i} \right|\left. {z\,} \right\|\,\, = \left| {z + i} \right|\left. {\,z} \right\|$$ is contained in or equal to
(B) The set of points z satisfying $$\left| {z + 4} \right| + \,\left| {z - 4} \right| = 10$$ is contained in or equal to
(C) If $$\left| w \right|$$= 2, then the set of points $$z = w - {1 \over w}$$ is contained in or equal to
(D) If $$\left| w \right|$$ = 1, then the set of points $$z = w + {1 \over w}$$ is contained in or equal to.

Column II

(p) an ellipse with eccentricity $${4 \over 5}$$
(q) the set of points z satisfying Im z = 0
(r) the set of points z satisfying $$\left| {{\rm{Im }}\,{\rm{z }}} \right| \le 1$$
(s) the set of points z satisfying $$\,\left| {{\mathop{\rm Re}\nolimits} \,\,z} \right| < 2$$
(t) the set of points z satisfying $$\left| {\,z} \right| \le 3$$
A
(A) - q, s ; (B) - p ; (C) - p, t ; (D) - q, r, s, t
B
(A) - q, r ; (B) - p ; (C) - p, s, t ; (D) - q, r, s, t
C
(A) - p, r ; (B) - p ; (C) - p, t ; (D) -q, r, s, t
D
(A) - p ; (B) - q ; (C) - r, s ; (D) -q, r, s, t
3
IIT-JEE 2009 Paper 1 Offline
+3
-1
Let $$z = \,\cos \,\theta \, + i\,\sin \,\theta$$ . Then the value of $$\sum\limits_{m = 1}^{15} {{\mathop{\rm Im}\nolimits} } ({z^{2m - 1}})\,at\,\theta \, = {2^ \circ }$$ is
A
$${1 \over {\sin \,{2^ \circ }}}$$
B
$${1 \over {3\sin \,{2^ \circ }}}$$
C
$${1 \over {2\sin \,{2^ \circ }}}$$
D
$${1 \over {4\sin \,{2^ \circ }}}$$
4
IIT-JEE 2009 Paper 1 Offline
+3
-1

Let $$z = x + iy$$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $$\overline z {z^3} + z{\overline z ^3} = 350$$ is

A
48
B
32
C
40
D
80
EXAM MAP
Medical
NEET