Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 29

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Suppose $A$ is a complex number and $n \in N,$ such that $A^{n} = {(A + 1)}^{n} = 1,$ then the least value of $n$ is

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Important Questions on Complex Numbers

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 30

The number of complex numbers z such that

|z| = 1

and

|\frac{z}{z} + \frac{z}{z}| = 1

is

(a r g (z) \in [0, 2 π])

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 31

Let

z, w

be complex numbers such that

z + i w = 0

and

\arg z w = π .

Then

\arg z

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 32

If

z = (3 + 7 i) (a + i b)

where

a, b \in Z - \{0\},

is purely imaginary, then the minimum value of

{|z|}^{2}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 33

If

(\cos θ + i \sin θ) (\cos 2 θ + i \sin 2 θ) . . . (\cos n θ + i \sin n θ) = 1,

then the value of

θ

is,

m \in Z

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 34

Given

z = {(1 + i \sqrt{3})}^{100},

then

[\frac{Re (z)}{Im (z)}]

equals

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 35

The expression

{[\frac{1 + \sin \frac{π}{8} + i \cos \frac{π}{8}}{1 + \sin \frac{π}{8} - i \cos \frac{π}{8}}]}^{8} =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 36

The number of complex numbers

z

satisfying

|z - 3 - i| = |z - 9 - i|

and

|z - 3 + 3 i| = 3

are

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 3 - Complex Numbers>Exercises>Q 37

P (z)

be a variable point in the Argand plane such that

|z| = minimum \{|z - 1|, |z + 1|\},

then

z + z

will be equal to