Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 5

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Let $z_{1}, z_{2}$ be two complex numbers represented by points on the circle $|z| = 1$ and $|z| = 2$ respectively, then

50% studentsanswered this correctly

Important Questions on Complex Numbers

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 6

If

α, β

be any two complex numbers such that

|\frac{α - β}{1 - \bar{α} β}| = 1

, then which of the following may be true :

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 7

Let

z, ω z

and

z + ω z

represent three vertices of

∆ A B C

, where

ω

is cube root unity, then

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 8

Which of the following complex numbers lies along the angle bisectors of the lines
$L_{1} : z = (1 + 3 λ) + i (1 + 4 λ)$

$L_{2} : z = (1 + 3 μ) + i (1 - 4 μ)$

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 9

Let

z

and

ω

are two complex numbers such that

| z | \leq 1, | ω | \leq 1

and

| z + i ω | = | z - i ω | = 2

, then

z

equals:

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 10

P (z)

be a variable point in the Argand plane such that

|z| = minimum \{|z - 1|, |z + 1|\},

then

z + z

will be equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 11

For two complex numbers

z_{1}

and

z_{2} : (a z_{1} + b {\bar{z}}_{1}) (c z_{2} + d {\bar{z}}_{2}) = (c z_{1} + d {\bar{z}}_{1}) (a z_{2} + b {\bar{z}}_{2})

if

(a, b, c, d \in R)

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 12

Which of the following locus of z on the complex plane represents a pair of straight lines?

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 13

If the complex numbers

z_{1}, z_{2}, z_{3}

represents vertices of an equilateral triangle such that

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

, then which of following is correct?