Real and Imaginary parts MCQ Quiz in বাংলা - Objective Question with Answer for Real and Imaginary parts - বিনামূল্যে ডাউনলোড করুন [PDF]

Last updated on Mar 12, 2025

পাওয়া Real and Imaginary parts उत्तरे आणि तपशीलवार उपायांसह एकाधिक निवड प्रश्न (MCQ क्विझ). এই বিনামূল্যে ডাউনলোড করুন Real and Imaginary parts MCQ কুইজ পিডিএফ এবং আপনার আসন্ন পরীক্ষার জন্য প্রস্তুত করুন যেমন ব্যাঙ্কিং, এসএসসি, রেলওয়ে, ইউপিএসসি, রাজ্য পিএসসি।

Latest Real and Imaginary parts MCQ Objective Questions

Top Real and Imaginary parts MCQ Objective Questions

Real and Imaginary parts Question 1:

If x + iy = , find x and y

  1. x =  and y = 
  2. x =  and y = 
  3. x =  and y = 
  4. x =  and y = 

Answer (Detailed Solution Below)

Option 2 : x =  and y = 

Real and Imaginary parts Question 1 Detailed Solution

Calculation:

x + iy = 

x + iy = 

x + iy = 

x + iy = 

∴ x =  and y = 

Real and Imaginary parts Question 2:

If  then the real values of x and y are given by

  1. x = -3, y = -1
  2. x = 3, y = - 1
  3. x = 3, y = 1
  4. x = 1, y = -3

Answer (Detailed Solution Below)

Option 2 : x = 3, y = - 1

Real and Imaginary parts Question 2 Detailed Solution

Concept:

1. A complex number (Z):  Complex number is the combination of a real number and an imaginary number. It is given by

Z = x + iy, where 'x' and 'y' are the real and imaginary parts of Z and

i = √-1 or i2 = -1

Re(Z) = x and Img(Z) = y

2. Two complex numbers will be equal if their real and imaginary part are equal.

Calculation:

Given that,

⇒(1 + i)(3x - ix) - 2i(3 - i) + (2 - 3i)(3y + iy) + i(3 + i) = 10i

⇒ 3x + 3xi - ix - i2x - 6i + 2i2 + 6y - 9iy + 2iy - 3yi2 + 3i + i2 = 10i

We know that,  i2 = -1

⇒ 3x + 2xi + x - 6i - 2 + 6y - 7yi + 3y + 3i -1 = 10i  

⇒ 4x + 9y − 3 + 2xi − 7yi − 13i = 0

⇒ 4x + 9y − 3 + (2x − 7y − 13)i = 0

On comparing the real part and imaginary part, we get

4x + 9y − 3 = 0     …… (1)

2x − 7y − 13 = 0  …… (2)

On solving both equations, we get

x = 3 and y = −1

Hence, the value of x, y is 3, −1.

Real and Imaginary parts Question 3:

If z = -z̅, then which one of the following is correct?

  1. The real part of z is zero.
  2. The imaginary part of z is zero.
  3. The real part of z is equal to imaginary part of z.
  4. The sum of real and imaginary parts of z is z.

Answer (Detailed Solution Below)

Option 1 : The real part of z is zero.

Real and Imaginary parts Question 3 Detailed Solution

Concept:

Let z = x + iy be any complex number. 

Conjugate of z:  

 

Calculations:

Let z = x + iy be any complex number. 

Given, z = -z̅

⇒ (x + iy) = - (x - iy) 

⇒ x + iy = - x + iy 

⇒ 2x = 0

i.e The real part of z is zero.

Hence, If z = -z̅, then the real part of z is zero.

 

Real and Imaginary parts Question 4:

If and is real, then the point represented by the complex number lies:

  1. either on the real axis or on a circle passing through the origin.
  2. on a circle with centre at the origin.
  3. either on the real axis or on a circle not passing through the origin.
  4. on the imaginary axis

Answer (Detailed Solution Below)

Option 1 : either on the real axis or on a circle passing through the origin.

Real and Imaginary parts Question 4 Detailed Solution

Calculation

and is real so imaginary Part is 0.

Let's say

⇒ 

On rationalizing

(Imaginary Part )

or

Hence option 1 is correct

Real and Imaginary parts Question 5:

4x + i(2x - y) = 8 - 4i , then x, y is 

  1. 2, 6
  2. 2, 8
  3. 8, 2
  4. 6, 2

Answer (Detailed Solution Below)

Option 2 : 2, 8

Real and Imaginary parts Question 5 Detailed Solution

Concept:

Equality of complex numbers.

Two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 are equal if and only if x1 = x2 and y1 = y2

Or Re (z1) = Re (z2and Im (z1) = Im (z2).

Calculations:

Given: 4x + i(2x - y) = 8 - 4i

Equating real part of the complex number 

⇒ 4x = 8

⇒ x = 2

Equating imaginary part of the complex number  

⇒ 2x - y = -4

Hence , option 2 is correct 

Real and Imaginary parts Question 6:

If a complex number is purely imaginary so find the value of x. The complex number is (x2 - 5x + 6) + i √17.

  1. 2, 3
  2. 3, 5
  3. 4, 2
  4. None of these

Answer (Detailed Solution Below)

Option 1 : 2, 3

Real and Imaginary parts Question 6 Detailed Solution

Concept:

A complex number z = x + iy

Real part of z = x, Imaginary part of z = y

If the Complex number is Purely imaginary so we can say that the Real part of a complex number is Zero.

If the Complex number is Purely real so we can say that the Imaginary part of a complex number is Zero.

Calculation:

Given: (x2 - 5x + 6) + i √17

For purely imaginary complex number real part is 0

So, x2 - 5x + 6 = 0

x2 - 3x - 2x + 6 = 0

x(x - 3) - 2(x - 3) = 0

(x - 3)(x - 2) = 0

Here, x = 2, 3

Real and Imaginary parts Question 7:

Find the real and imaginary part of the complex number 

  1. 1, 1
  2. -1, 1
  3. 0, 1
  4. 0, -1

Answer (Detailed Solution Below)

Option 4 : 0, -1

Real and Imaginary parts Question 7 Detailed Solution

Concept:

Equality of complex numbers.

Two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2 are equal if and only if x1 = x2 and y1 = y2

Or Re (z1) = Re (z2and Im (z1) = Im (z2).

 

Calculations:

Given complex number 

Multiplying the numerator and denominator with 1 - i

= -i

So, z = 0 - i

∴ Re (z) = 0 and Im (z) = -1

Hence,option 4 is correct  

Real and Imaginary parts Question 8:

What is the value of  where ?

  1. 24
  2. 25
  3. 5√2
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 5√2

Real and Imaginary parts Question 8 Detailed Solution

Formula Used: 

(a + b) (a - b) = a2 - b2

i2 = -1

Calculation:

Let x =, where 

Squaring both sides,

x2

x2

x2 = 

x2 = 

x2 = 

x = 

Real and Imaginary parts Question 9:

If (a + ib)(c + id)(e + if)(g + ih) = A + iB, then (a2 + b2(c2 + d2)(e2 + f2)(g2 + h2) is equal to

  1. A2 - B2
  2. A2 + B2
  3. A4 + B4
  4. A4 - B4

Answer (Detailed Solution Below)

Option 2 : A2 + B2

Real and Imaginary parts Question 9 Detailed Solution

Concept:

|z1.z2| = |z1|.|z2|

If z = x + iy, then |z| = √(x2 + y2)

Calculation:

Given, 

(ib)(id)(if)(ih) = iB

Now taking modulus both sides we get,

|(a + ib)(c + id)(e + if)(g + ih)| = |A + iB|

⇒ |(a + ib)|.|(c + id)|.|(e + if)|.|(g + ih)| = |A + iB|

⇒ √(a2 + b2) .√(c2 + d2​) .√(e2 + f2​) .√(g2 + h2​) = √(A2 + B2​) 

Squaring both sides,

(a2 + b2(c2 + d2)(e2 + f2)(g2 + h2) = A2 + B2

∴ The correct answer is option (2).

Real and Imaginary parts Question 10:

If , then

  1. Re(z) = 0
  2. lm(z) = 0
  3. Re(z) > 0, lm(z) = 0
  4. Re(z) > 0, lm(z) < 0

Answer (Detailed Solution Below)

Option 2 : lm(z) = 0

Real and Imaginary parts Question 10 Detailed Solution

Concept:

cos θ + i sin θ = e

cos(π/6) = √3/2, sin(π/6) = 1/2

cos(5π/6) = -√3/2, sin(5π/6) = 1/2

Calculation:

Given, 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ Im(z) = 0 and Re(z)

∴ The correct answer is option (2).

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