Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 1>Q 36

EASY

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IMPORTANT

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If $z_{1}, z_{2}, z_{3}$ are vertices of an equilateral triangle with orthocentre $z_{0}$ then $z_{1}^{2} + z_{2}^{2} + z_{3}^{2} = k z_{0}^{2}$ , where $k \in N$ , then $k$ is equal to

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Important Questions on Complex Numbers

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 1

If the area of the triangle on the complex plane formed by the

3

points

z, z + i z

and

i z

is

200,

then the value of

3 |z|

must be equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 2

If

z

is non-real and

i = \sqrt{- 1},

then

\sin^{- 1} (\frac{1}{i} (z - 1))

be the angle of a triangle, if

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Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 3

If

|z_{1}| = |z_{2}| = \dots \dots |z_{n}| = 1,

then the value of

|z_{1} + z_{2} + \dots \dots z_{n}| - |\frac{1}{z_{1}} + \frac{1}{z_{2}} + \dots \dots + \frac{1}{z_{n}}|

is

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 4

If

Re (\frac{z + 2 i}{z + 4}) = 0,

then

z

lies on a circle with centre

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 5

The imaginary part of

(z - 1)

(\cos α - i \sin α) + {(z - 1)}^{- 1} \times (\cos α + i \sin α)

is zero if

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 6

Consider two complex numbers

α

and

β

as

α = {(\frac{a + b i}{a - b i})}^{2} + {(\frac{a - b i}{a + b i})}^{2},

where

a, b \in R

and

β = \frac{z - 1}{z + 1},

where

|z| = 1,

then

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Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 7

If

z = 1 + i \sqrt{3}

, then

| \arg (z) | + | \arg (\bar{z}) |

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 8

Let

S = \{z \in C : z (i z_{1} - 1) = z_{1} + 1, |z_{1}| < 1\}

. Then, for all

z \in S,

which one of the following is always true?