New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2013 · Shift 2 · Q36

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2013 · Shift 2 · Q36

Complex Numbers question

2013 · Shift 2 · Q36

JEE AdvancedMathematicsComplex NumbersMCQ+4 / −1

Let

S = {S_1} \cap {S_2} \cap {S_3}

, where

{S_1} = \left\{ {z \in C:\left| z \right| \lt 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im} olimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] \gt 0} \right\}

and

{S_3} = \left\{ {z \in C:{\mathop{\rm Re} olimits} z \gt 0} \right\}\,

.

\,\mathop {\min }\limits_{z \in S} \left| {1 - 3i - z} \right| =

A
${{2 - \sqrt 3 } \over 2}$
B
${{2 + \sqrt 3 } \over 2}$
C
${{3 - \sqrt 3 } \over 2}$
D
${{3 + \sqrt 3 } \over 2}$

More from Complex Numbers

Let $S = S_{1} \cap S_{2} \cap S_{3}$ , where $S_{1} = {z \in C : ∣ z ∣ < 4}, S_{2} = {z \in C : Im [\frac{z - 1 + 3 i}{1 - 3 i}] > 0}$ and $S_{3} = {z \in C : Re (z) > 0}$ …2013 · MCQ
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 value2012 · MCQ
If z is any complex number satisfying $∣ z - 3 - 2 i ∣ \leq 2$ , then the minimum value of $∣ 2 z - 6 + 5 i ∣$ is2011 · Numerical
Let $ω = e^{\frac{iπ}{3}}$ , and a, b, c, x, y, z be non-zero complex numbers such that $a + b + c = x a + bω + c ω^{2} = y a + b ω^{2} + c ω = z$ Then the value of $\frac{∣ x ∣ ^{2} + ∣ y ∣ ^{2} + ∣ z ∣ ^{2}}{∣ a ∣ ^{2} + ∣ b ∣ ^{2} + ∣ c ∣ ^{2}}$ …2011 · Numerical
Let $z_{1}$ and $z_{2}$ be two distinct complex number and let z =( 1 - t) $z_{1}$ + t $z_{2}$ for some real number t with 0 < t < 1. IfArg (w) denote the principal argument of a non-zero complex number w, then2010 · Multiple correct
Let $z_{1}$ and $z_{2}$ be two distinct complex numbers let $z = (1 - t) z_{1} + t z_{2}$ for some real number t with $0 I f$ \operatorname{Arg}(w) $d e n o t es t h e p r in c i p a l a r g u m e n t o f an o n z er oco m pl e x n u mb er$ w$, then :2010 · Multiple correct
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 $∣ z - i ∣ z ∥ = ∣ z + i ∣ z ∥$ …2010 · MCQ
Let $z = x + i y$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation $\overline{z} z^{3} + z \overline{z}^{3} = 350$ is2009 · MCQ