Test: Complex Number- 2


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


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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)= 2x 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 – 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:

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