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

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IMPORTANT

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Let ${}^{'}z^{'}$ be a complex number and ${}^{'}a^{'}$ be a real parameter such that $z^{2} + a z + a^{2} = 0$ , then which is of the following is not true?

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Important Questions on Complex Numbers

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JEE Main

IMPORTANT

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

Let

z = x + i y

. Then locus of moving point

P (z)

such that

\frac{1 + \bar{z}}{z} \in R

is (where

i^{2} = - 1

)

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JEE Main

IMPORTANT

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

Let

A (z_{1})

and

B (z_{2})

are two distinct non-real complex numbers in the argand plane such that

\frac{z_{1}}{z_{2}} + \frac{z_{1}}{\bar{z_{2}}} = 2

. Then the value of

| ∠ A B O |

is

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JEE Main

IMPORTANT

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

Complex numbers

z_{1}

and

z_{2}

satisfy

| z_{1} | = 2

and

| z_{2} | = 3 .

If the included angle of their corresponding vectors is

60 °

then the value of

19 {|\frac{z_{1} - z_{2}}{z_{1} + z_{2}}|}^{2}

is

HARD

JEE Main

IMPORTANT

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

Let

A (2, 0)

and

B (z)

are two points on the circle

|z| = 2 . M (z^{'})

is a point on

A B

. If the point

{\bar{z}}^{'}

lies on the median of the triangle

O A B

, where

O

is origin, then

\arg (z^{'})

is

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JEE Main

IMPORTANT

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

If

A (z_{1}), B (z_{2}), C (z_{3})

are vertices of a triangle such that

z_{3} = \frac{z_{2} - i z_{1}}{1 - i}

and

|z_{1}| = 3, |z_{2}| = 4 and |z_{2} + i z_{1}| = |z_{1}| + |z_{2}|

, then the area of triangle

A B C

is

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JEE Main

IMPORTANT

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

Let

O, A, B

be three collinear points such that

O A \cdot O B = 1

. If

O

and

B

represent the complex number

O

and

Z

then

A

represents

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JEE Main

IMPORTANT

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

If the tangents at

z_{1}, z_{2}

on the circle

|z - z_{0}| = r

intersect at

z_{3}

, then

\frac{(z_{0} - z_{1}) (z_{0} - z_{2})}{(z_{0} - z_{1}) (z_{3} - z_{2})}

equals

HARD

JEE Main

IMPORTANT

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

If

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

are the vertices of

△ A B C

, which is not a right-angled triangle, taken in anti-clockwise direction and

z_{0}

is the circumcentre, then

(\frac{z_{0} - z_{1}}{z_{0} - z_{2}}) \frac{\sin 2 A}{\sin 2 B} + (\frac{z_{0} - z_{3}}{z_{0} - z_{2}}) \frac{\sin 2 C}{\sin 2 B}

is equal to