Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 3

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Earn 100

Given the complex number $z = 2 + 3 i$ , represent the complex numbers $z, i z,$ and $z + i z$ in Argand diagram.

Important Questions on Complex Numbers

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 4

Given the complex number $z = 2 + 3 i$ , represent the complex numbers $z, - i z,$ and $z - i z$ in Argand diagram.

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 5

If

z_{1} = 1 - 3 i, z_{2} = - 4 i, and z_{3} = 5

, show that

(z_{1} z_{2}) z_{3} = z_{1} (z_{2} z_{3})

.

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 6

If $z_{1} = 1 + 2 i, z_{2} = 1 - 3 i$ and $z_{3} = 2 + 4 i$ then, the points on the Argand diagram representing $z_{1} z_{2} z_{3}, 2 z_{1} z_{2} z_{3}, - 7 z_{1} z_{2} z_{3}$ are:

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 7

If

{(\frac{1 + i}{1 - i})}^{x} = 1,

then

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 8

If

n

is any integer, then

i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}

is equal to

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 9

The value of

(1 + i) (1 + i^{2}) (1 + i^{3}) (1 + i^{4})

is

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 10

If

x + i y = (2 + 3 i) (2 - 3 i) (1 + i)^{2},

then

x

is equal to

EASY

12th Tamil Nadu Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 2 - Complex Numbers>Exercise>Q 11

The least positive integer

n

for which

(1 + i)^{2 n} = (1 - i)^{2 n}

is