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

HARD

JEE Main

IMPORTANT

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Let $z \in C$ be such that $|z| < 1 .$ If $ω = \frac{5 + 3 z}{5 (1 - z)},$ then:

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Important Questions on Complex Numbers

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:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 9th January 2019 Shift 2>Q 52

Let

z_{0}

be a root of quadratic equation,

x^{2} + x + 1 = 0 .

If

z = 3 + 6 i z_{0}^{81} - 3 i z_{0}^{93}

, then

a r g

(z)

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 8th April 2019 Shift 2>Q 53

If

z = \frac{\sqrt{3}}{2} + \frac{i}{2} (i = \sqrt{- 1}),

then

{(1 + i z + z^{5} + i z^{8})}^{9}

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 10th April 2019 Shift 1>Q 54

If

a > 0

and

z = \frac{{(1 + i)}^{2}}{a - i}

, has magnitude

\sqrt{\frac{2}{5}}

, then

\bar{z}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 10th April 2019 Shift 2>Q 55

If

z

and

ω

are two complex numbers such that

|z ω| = 1

and

a r g (z) - a r g (ω) = \frac{π}{2}

, then:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 10th January 2019 Shift 1>Q 56

Let

z_{1}

and

z_{2}

be any two non-zero complex numbers such that

3 |z_{1}| = 4 |z_{2}| .

If

z = \frac{3 z_{1}}{2 z_{2}} + \frac{2 z_{2}}{3 z_{1}}

then maximum value of

|z|

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 4 - Complex Numbers>JEE Main - 10th January 2019 Shift 2>Q 57

Let

z = {(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} + {(\frac{\sqrt{3}}{2} - \frac{i}{2})}^{5} .

If

R (z)

and

I (z)

respectively denote the real and imaginary parts of

z,

then