Complex Numbers and Quadratic Equations Online Objective Test | Complex Numbers and Quadratic Equations Online Objective Test

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q1. The equation | 4z − 1 | = 4 | z − 5 | represents :

A. an ellipse

B. a straight line

C. a parabola

D. a circle

Answer : Option B
Explaination / Solution:

Squaring on both sides we get

We have x= a constant is a straight line parallel to Y-axis.

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q2. If

{(- 1 + \sqrt{3} i)}^{n} + {(- 1 - \sqrt{3} i)}^{n} = 2^{n} α

then

α

is equal to :

A. None of these

B. -1

C. 2

Answer : Option D
Explaination / Solution:

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q3. If ( x + iy ) ( 3 – 4i ) = (5 + 12i ) , then

\sqrt{x^{2} + y^{2}} =

A. 16

B. 13/5

C. 5/13

D. 65

Answer : Option B
Explaination / Solution:

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q4. he locus of the equation

| \frac{3 z - 1}{z - 1} | = 1

A. a circle

B. a straight line

C. an ellipse

D. none of these.

Answer : Option A
Explaination / Solution:

We have this is a circle with centre (1/4,0) and radius =1/4.

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q5.

\sqrt{- 8} \sqrt{- 18} \sqrt{- 4}

A. -24

B. -24i

C. 24

D. 24i

Answer : Option B
Explaination / Solution:

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q6. If

α = \frac{z}{\bar{z}},

then

| α |

is equal to:

A. 1

B. None of these

C. -1

D. 0

Answer : Option A
Explaination / Solution:

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q7. The smallest positive integer n for which

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

A. 2

B. 8

C. None of these

D. 4

Answer : Option D
Explaination / Solution:

By inspection we have the smallest positive integer such that

i^{n} = 1

is n=4.

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q8. If

z = {(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} + {(\frac{\sqrt{3}}{2} - \frac{i}{2})}^{5},

then

A. Im ( z ) < 0

B. Im ( z ) = 0

C. Re ( z ) >0

D. None of these

Answer : Option B
Explaination / Solution:

which is purely real [ imaginary part of z=0]

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q9. If the cube roots of unity are 1,

ω, ω^{2},

then roots of the equation

{(x - 1)}^{3} + 8 = 0

are :

A. none of these

B. −1,1-2ω,1 -2ω2

C. -1 ,-1 , -1

D. −1,−1+2ω,1+2ω2

Answer : Option B
Explaination / Solution:

# Complex Numbers and Quadratic Equations # CBSE 11th Mathematics Prepare / Learn

Q10. Arg. ( x ) , x ∈ R and x < 0 is

A. π

B. 3π/2

C. 0

D. π/2

Answer : Option A
Explaination / Solution:

Given x $\in$ R and x $<$ 0, therefore the number is $- x + 0 i$ and this will be a point inthe second quadrant as x is negative

We have arg( $- x + 0 i$ = $θ =$ $\tan^{- 1} | \frac{y}{x} | = \tan^{- 1} | \frac{0}{- 1} | = \tan^{- 1} 0 = 0$

We have in the second quadrant the principal value of argument= $Π - θ = Π - 0 = Π$

Hence Arg. ( x ) , x $\in$ R and x $<$ 0 is $π$

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