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# Test: Complex Number- 2

## 10 Questions MCQ Test Quantitative Aptitude (Quant) | Test: Complex Number- 2

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

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 – ω2)7 equals :

Solution:
QUESTION: 4

Value of ω1999 + ω299 + 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 z3 – 2z+ 4z – 8 = 0 then :

Solution:

z3 – 2z2 + 4z – 8 = 0
⇒ (z − 2)(z2 + 4)=0
⇒ z − 2 = 0    : z = 2
⇒ z2 + 4 = 0  : z = 2i, z = −2i
∴ z = 2, z = 2i, z = −2i
∴ ∣z∣ = 2

QUESTION: 8

i1 + i2 + i3 + i4 + ……… + i1000 =

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,ω2 then 1 + ω + ω=

Solution:
QUESTION: 10

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

Solution: