EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 7th January 2020 Shift 1>Q 43

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JEE Main

IMPORTANT

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If $R e (\frac{z - 1}{2 z + i}) = 1,$ where $z = x + i y,$ then the point $(x, y)$ lies on a

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Important Questions on Complex Numbers

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 7th January 2020 Shift 2>Q 44

If

\frac{3 + i s i n θ}{4 - i c o s θ}, θ \in [0, 2 π],

is a real number, then an argument of

s i n θ + i c o s θ

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 8th January 2020 Shift 1>Q 45

If the equation

x^{2} + b x + 45 = 0, b \in R

has conjugate complex roots and they satisfy

|z + 1| = 2 \sqrt{10},

then

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th January 2020 Shift 1>Q 46

Let

z

be a complex number such that

|\frac{z - i}{z + 2 i}| = 1

and

|z| = \frac{5}{2}

. Then, the value of

|z + 3 i|

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th January 2020 Shift 2>Q 47

If

z

is a complex number satisfying

|R e (z)| + |I m (z)| = 4,

then

|z|

cannot be

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th April 2019 Shift 1>Q 48

All the points in the set

S = \{\frac{α + i}{α - i}, α \in R\}, i = \sqrt{- 1}

lie on a

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th April 2019 Shift 2>Q 49

Let

z \in C

be such that

|z| < 1 .

If

ω = \frac{5 + 3 z}{5 (1 - z)},

then:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th January 2019 Shift 1>Q 50

Let

α

and

β

be the roots of the equation

x^{2} + 2 x + 2 = 0,

then

α^{15} + β^{15}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th January 2019 Shift 1>Q 51

Let

A = \{θ \in (- \frac{π}{2}, π) : \frac{3 + 2 i s i n θ}{1 - 2 i s i n θ} is purely imaginary\} .

Then the sum of the elements in

A

is: