Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 16

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If the vertices of an equilateral triangle are situated at $z = 0, z = z_{1}, z = z_{2}$ , then which of the following is/are true -

50% studentsanswered this correctly

Important Questions on Complex Numbers

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 17

Value(s) of

(- i)^{\frac{1}{3}}

is/are -

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 18

Centre of square

A B C D

is at

z = 0

. If affix of vertex

A

is

z_{1}

, centroid of triangle

A B C

can be:

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-2>Q 19

If

ω

is an imaginary cube root of unity, then a root of equation

|\begin{matrix} x + 1 & ω & ω^{2} \\ ω & x + ω^{2} & 1 \\ ω^{2} & 1 & x + 2 \end{matrix}| = 0

, can be

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 11

Let

z_{1}

and

z_{2}

be two complex numbers such that

|\frac{z_{1} - 2 z_{2}}{2 - z_{1} {\bar{z}}_{2}}| = 1

and

|z_{2}| \neq 1

, find

|z_{1}|

.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 12

Let

A = \{a \in R ∣

the equation

(1 + 2 i) x^{3} - 2 (3 + i) x^{2} + (5 - 4 i) x + 2 a^{2} = 0

has at least one real root

}

. Find the value of

\frac{1}{5} \sum_{a \in A} a^{2}

.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 13

Let

ω

and

z

be complex numbers such that

| ω | = 1

and

| z | = 10

. Let

θ = \arg (\frac{ω - z}{z})

. The maximum possible value of

\tan^{2} θ

can be written as

\frac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

\frac{1}{8} (p + q)

.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 14

If the biquadratic

x^{4} + a x^{3} + b x^{2} + c x + d = 0 (a, b, c, d \in R)

has

4

non real roots, two with sum

3 + 4 i

and the other two with product

13 + i

. Find the value of '

b

'.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 6 - Complex Numbers>EXERCISE-3>Q 15

Number of ordered pair

(z, ω)

satisfying

z + \frac{1}{\bar{z}} = ω

and

ω + \frac{1}{\bar{ω}} = z

is/ are equal to