Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 13

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

If $x = - 5 + 2 \sqrt{- 4}$ , then the value of the expression $x^{4} + 9 x^{3} + 35 x^{2} - x + 4$ is equal to

80.52% studentsanswered this correctly

Important Questions on Complex Numbers

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 15

It is given that the equation

| z |^{2} - 2 i z + 2 α (λ + i) = 0

possesses a solution for all

α \in R,

then the number of integral value(s) of '

λ

' for which it is true is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 1

If

a, b, c

are real numbers and

z

is a complex number such that,

a^{2} + b^{2} + c^{2} = 1

and

b + i c = (1 + a) z

then

\frac{1 + i z}{1 - i z}

equals.

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 2

If

z

satisfies

| z - 1 | < | z + 3 |,

then

ω = 2 z + 3 - i

satisfies

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 3

If

| z + ω |^{2} = | z |^{2} + | ω |^{2}

, where

z

and

ω

are complex numbers, then

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 4

Let

z_{1}, z_{2}

be two complex numbers represented by points on the circle

|z| = 1

and

|z| = 2

respectively, then

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 5

Let complex number

z

satisfy

|z - \frac{2}{z}| = 1,

then

| z |

can take all values except

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 6

If

z_{1} = a + i b

and

z_{2} = c + i d

are complex numbers such that

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

and

Re (z_{1} z_{2}) = 0

, then the pair of complex numbers

ω_{1} = a + i c

and

ω_{2} = b + i d

satisfies

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>Assignment>Q 7

If

z_{1}, z_{2}

be two complex numbers satisfying the equation

|\frac{z_{1} + z_{2}}{z_{1} - z_{2}}| = 1

, then