If 1 - i z z - i = 1 , then z lies on

a line not passing through origin

MEDIUM

Earn 100

What type of sentence is the following: 'She is not only intelligent but also hardworking.'?

50% studentsanswered this correctly

Important Questions on Complex Numbers and Quadratic Equations

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The set of cubes of natural numbers is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1}), where i = \sqrt{- 1},

equals

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Two finite sets respectively have

x

and

y

number of elements. The total number of sub sets of the first is

56

more than the total no. of sub sets of the second. The value of

x, y

are respectively __________

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

For all complex numbers

z

of the form

1 + i α, α \in R,

z^{2} = x + i y,

then

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The following Venn diagram indicates

Question Image

HARD

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Let

a > 0, a \neq 1

. Then, the set

S

of all positive real numbers

b

satisfying

(1 + a^{2}) (1 + b^{2}) = 4 a b

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Which of the following is an empty set?

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Let

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} .

Then the number of subsets of

A

containing two or three elements is

HARD

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The maximum value of

|z|

where

z

satisfies the condition

|z + \frac{2}{z}| = 2

, is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The equation, whose roots are

i, \frac{1 + i}{\sqrt{2}}, \frac{i - 1}{\sqrt{2}},

their conjugates,

- 1 and 1

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

z

is a complex number such that

Re (z) = I m (z)

, then

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

(3 + i) z = (3 - i) \bar{z}

, then the complex number

z

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

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

then

z

lies on

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1})

, where

i = \sqrt{- 1}

, equals

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The complex number which satisfy the equation

z + \sqrt{2} |z + 1| + i = 0

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of

\sum_{n = 0}^{100} i^{n!}

equals (where

i = \sqrt{- 1}

)

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The relation between the real numbers

a

and

b

, which satisfy the equation

\frac{1 - i x}{1 + i x} = a - i b

, for some real value of

x

, is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Let

z

be a complex number such that the imaginary part of

z

is nonzero and

a = z^{2} + z + 1

is real. Then

a

cannot take the value

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If $a = \cos α + i \sin α, b = \cos β + i \sin β$ , $c = \cos γ + i \sin γ$ and $\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 1$ , then $\cos (β - γ) + \cos (γ - α) + \cos (α - β)$ is equal to $(where i = \sqrt{- 1})$

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Evaluate

{(- \sqrt{- 1})}^{4 n + 3}, n \in N

What type of sentence is the following: 'She is not only intelligent but also hardworking.'?

Important Questions on Complex Numbers and Quadratic Equations

Learn and Prepare for any exam you want !