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Complex Numbers question

2010 · Shift 2 · Q21

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2010 · Shift 2 · Q21

Complex Numbers question

2010 · Shift 2 · Q21

JEE AdvancedMathematicsComplex NumbersMCQ+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} olimits} \,\,z} \right| \lt 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

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