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

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IMPORTANT

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If $Re (\frac{z + 2 i}{z + 4}) = 0,$ then $z$ lies on a circle with centre

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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 5

The imaginary part of

(z - 1)

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

is zero if

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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?

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Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 9

The argument of

(z - a) (\bar{z} - b)

is equal to that of

\frac{(\sqrt{3} + i) (1 + \sqrt{3} i)}{1 + i}

where

a, b

are real numbers. If the locus of

z

in the Argand diagram is a circle with its centre at

\frac{(3 + i)}{2}

, then the ordered pair

(a, b)

is

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Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 10

The least value of

{|z - 3 - 4 i|}^{2} + {|z + 2 - 7 i|}^{2} + {|z - 5 + 2 i|}^{2}

occurs when

z

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 11

If

z_{1}, z_{2}

are complex numbers such that

Re (z_{1}) = |z_{1} - 2|

,

Re (z_{2}) = |z_{2} - 2|

and

\arg (z_{1} - z_{2}) = \frac{π}{3},

then

Im (z_{1} + z_{2}) = ?

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 5 - Complex Numbers>Level 2>Q 12

If

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

are complex numbers such that

|z_{1}| = |z_{2}| = |z_{3}| = 1

, then

{|z_{1} - z_{2}|}^{2} + {|z_{2} - z_{3}|}^{2} + {|z_{3} - z_{1}|}^{2}

cannot exceed.