EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2018 (04-May Shift-1)>Q 23

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The points in the Argand plane given by $Z_{1} = - 3 + 5 i, Z_{2} = - 1 + 6 i, Z_{3} = - 2 + 8 i, Z_{4} = - 4 + 7 i$ form a

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Important Questions on Complex Numbers

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2018 (04-May Shift-1)>Q 1

When

n = 8

,

{(\sqrt{3} + i)}^{n} + {(\sqrt{3} - i)}^{n} =

HARD

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2019 (03-May Shift-2)>Q 2

If the point

(\frac{k - 1}{k}, \frac{k - 2}{k})

lies on the locus of

z

satisfying the inequality

|\frac{z + 3 i}{3 z + i}| < 1,

then the interval in which

k

lies is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2019 (03-May Shift-2)>Q 3

The solution set of the inequation

3^{x} + 3^{1 - x} - 4 < 0,

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2019 (03-May Shift-2)>Q 4

If the amplitude of

(z - 1 - 2 i)

is

\frac{π}{3}

, then the locus of

z

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET - 5 August 2021 Shift 1>Q 5

If

z_{1} = 1 - 2 i, z_{2} = 1 + i

and

z_{3} = 3 + 4 i,

then

|(\frac{1}{z_{1}} + \frac{2}{z_{2}}) \frac{z_{3}}{z_{2}}| =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET - 5 August 2021 Shift 1>Q 6

If

2 + 2 \sqrt{3} i = k (\cos θ + i \sin θ), (k > 0),

then

\frac{1}{\sqrt{3}} [\cos 6 θ + i \sin 6 θ] =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2020 (9-Sep Shift-1)>Q 7

Let

z \in C

and

i = \sqrt{- 1}

, if

a, b, c \in (0, 1)

be such that

a^{2} + b^{2} + c^{2} = 1

and

b + i c = (1 + a) z

, then

\frac{1 + i z}{1 - i z} =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Complex Numbers>TS EAMCET 2020 (9-Sep Shift-1)>Q 8

If

A = \{z = x + i y / real part of \frac{\bar{z} - 1}{z - i} = 2\}

then the locus of the point

P (x, y)

in the Cartesian plane is