EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Advanced Paper 1 - 2018>Q 13

HARD

JEE Advanced

IMPORTANT

Earn 100

For a non-zero complex number $z$ , let $\arg (z)$ denote the principal argument with $- π < a r g (z) \leq π$ then, which of the following statement(s) is (are) FALSE?

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Important Questions on Complex Numbers

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Advanced Paper 1 - 2017>Q 14

Let

a, b, x

and

y

be real numbers such that

a - b = 1

and

y \neq 0

. If the complex number

z = x + i y

satisfies

Im (\frac{a z + b}{z + 1}) = y,

then which of the following is (are) possible value (s) of

x ?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Advanced Paper 1 - 2013>Q 16

Let complex numbers

α

and

\frac{1}{\bar{α}}

lie on circles

{(x - x_{0})}^{2} + {(y - y_{0})}^{2} = r^{2}

, and

{(x - x_{0})}^{2} + {(y - y_{0})}^{2} = 4 r^{2}

, respectively. If

z_{0} = x_{0} + i y_{0}

satisfies the equation

2 {|z_{0}|}^{2} = r^{2} + 2

, then

|α| =