EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2018>Q 9

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If $z_{1}$ and $z_{2}$ be two non-zero complex numbers such that $\frac{z_{1}}{z_{2}} + \frac{z_{2}}{z_{1}} = 1,$ then the origin and the points represented by $z_{1}$ and $z_{2}$

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Important Questions on Complex Numbers

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2019>Q 1

The general value of the real angle

θ,

which satisfies the equation,

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

is given by, (assuming

k

is an integer)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2019>Q 2

If

θ \in ℝ

and

\frac{1 - i \cos θ}{1 + 2 i \cos θ}

is real number, then

θ

will be (when

I :

Set of integers)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2018>Q 3

If

Z_{r} = \sin \frac{2 π r}{11} - i \cos \frac{2 π r}{11},

then

\sum_{r = 0}^{10} Z_{r}

is equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2019>Q 4

Let

z

be a complex number such that the principal value of argument,

\arg z > 0 .

Then,

\arg z - \arg (- z)

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2019>Q 5

For any non-zero complex number

z,

the minimum value of

| z | + | z - 1 |

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2018>Q 6

Let

z_{1}

and

z_{2}

be complex numbers such that

z_{1} \neq z_{2}

and

|z_{1}| = |z_{2}| .

If

Re (z_{1}) > 0

and

Im (z_{2}) < 0,

then

\frac{z_{1} + z_{2}}{z_{1} - z_{2}}

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2020>Q 7

The number of complex numbers

p

such the

| p | = 1

and imaginary part of

p^{4}

is

0,

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>WBJEE 2020>Q 8

The equation

z \bar{z} + (2 - 3 i) z + (2 + 3 i) \bar{z} + 4 = 0

represents a circle of radius