Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 2

MEDIUM

JEE Main

IMPORTANT

Earn 100

Let $z_{1}$ and $z_{2}$ be two complex numbers with $α$ and $β$ be their principal arguments, such that $α + β > π$ . Then principal $a r g (z_{1} z_{2})$ is given by

42.86% studentsanswered this correctly

Important Questions on Complex Numbers

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 3

Let arg

(z_{k}) = \frac{(2 k + 1) π}{n}

where

k = 1, 2, 3, 4 . . ., n

. If arg

(z_{1} z_{2} z_{3} . . . z_{n}) = π

, then

n

must be of form

(m \in I)

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 4

Suppose two complex numbers

z = a + i b

;

w = c + i d

satisfy the equation

\frac{z + w}{z} = \frac{w}{z + w}

, then

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 5

If

|z| = 1 and z \neq \pm 1

, then one of the possible values of

a r g (z) - a r g (z + 1) - a r g (z - 1)

, is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 6

If

\arg (z^{\frac{3}{8}}) = \frac{1}{2} \arg (z^{2} + \bar{z} z^{\frac{1}{2}}),

then which of the following is not possible?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 7

z_{1}, z_{2}

are two distinct points in complex plane such that

2 |z_{1}| = 3 |z_{2}| and z \in C

be any point

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

, then

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 8

Let

z_{1} = x_{1} + i y_{1}, z_{2} = x_{2} + i y_{2}

be complex numbers in fourth quadrant of Argand plane and

|z_{1}| = |z_{2}| = 1, R e (z_{1} z_{2}) = 0

. The complex numbers

z_{3} = x_{1} + i x_{2,} z_{4} = y_{1} + i y_{2,} z_{5} = x_{1} + i y_{2,} z_{6} = x_{2} + i y_{1,}

will always satisfy

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 9

If the imaginary part of

\frac{z - 3}{e^{iθ}} + \frac{e^{iθ}}{z - 3}

is zero, then

z

can lie on

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 1

If

α, β, γ \in \{1, ω, ω^{2}\}

(where

ω

and

ω^{2}

are imaginary cube roots of unity), then number of triplets

(α, β, γ)

such that

|\frac{a α + b β + c γ}{a β + b γ + c α}| = 1

is