Description

This mock test of Test: Complex Number- 2 for Quant helps you for every Quant entrance exam.
This contains 10 Multiple Choice Questions for Quant Test: Complex Number- 2 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Test: Complex Number- 2 quiz give you a good mix of easy questions and tough questions. Quant
students definitely take this Test: Complex Number- 2 exercise for a better result in the exam. You can find other Test: Complex Number- 2 extra questions,
long questions & short questions for Quant on EduRev as well by searching above.

QUESTION: 1

Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for **"Complex Number"** under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.

1. Number of solutions to the equation (1 –i)^{x }= 2^{x} is :

Solution:

QUESTION: 2

If , arg(z) < 0, then arg(-z) – arg(z) =

Solution:

Let z = e-iθ

= cos(θ)−isin(θ)

arg(z)=−θ

arg(z)<0.

Now −z = −cos(θ)+isin(θ)

arg(−z) = π−θ

Hence arg(−z)−arg(z)

= π−θ−(−θ)

= π

QUESTION: 3

If ω is an imaginary cube root of unity, then (1 + ω – ω^{2})^{7} equals :

Solution:

QUESTION: 4

Value of ω^{1999} + ω^{299 }+ 1 is :

Solution:

QUESTION: 5

Principal argument of z = -√3+i is :

Solution:

Ar(z)= tan(1/√3)

= π/6

since it lies in second quadrant

so it will be = π -π/6

= 5π/6

QUESTION: 6

Which one is not a root of the fourth root of unity.

Solution:

QUESTION: 7

If z^{3} – 2z^{2 }+ 4z – 8 = 0 then :

Solution:

z^{3} – 2z^{2} + 4z – 8 = 0

⇒ (z − 2)(z^{2} + 4)=0

⇒ z − 2 = 0 : z = 2

⇒ z^{2} + 4 = 0 : z = 2i, z = −2i

∴ z = 2, z = 2i, z = −2i

∴ ∣z∣ = 2

QUESTION: 8

i^{1} + i^{2} + i^{3} + i^{4} + ……… + i^{1000} =

Solution:

i = √-1

i = i

i² = (√-1)² = - 1

i³ = i² * i = - 1 * i = - i

i⁴ = (i²)² = (-1)² = 1

i + i² + i³ + i⁴

= i - 1 - i + 1

= i - i + 1 - 1

= 0 + 0

= 0

i + i² + i³ + i⁴ = 0

⇒ i1 + i2 + i3 + i4 + ……… + i1000

⇒ 0 + 0 +........0(250 times)

⇒ 0

QUESTION: 9

If the cube roots of unity are 1,ω,ω^{2} then 1 + ω + ω^{2 }=

Solution:

QUESTION: 10

The small positive integer ‘n’ for which (1+i)^{2n }= (1-i)^{2n }is :

Solution:

### Introduction to Complex Number

Doc | 7 Pages

### Revision Notes - Complex Number

Doc | 3 Pages

### Complex Number With Examples

Doc | 6 Pages

### Solved Examples - Complex Number

Doc | 1 Page

- Test:- Complex Number - 2
Test | 19 questions | 60 min

- Test: Complex Number- 2
Test | 10 questions | 15 min

- Test: Complex Number- 1
Test | 5 questions | 10 min

- Complex Number MCQ Level - 2
Test | 10 questions | 45 min

- Complex Number NAT Level - 2
Test | 10 questions | 45 min