Modulus of Complex Number MCQ Quiz - Objective Question with Answer for Modulus of Complex Number - Download Free PDF

Last updated on Apr 11, 2025

Latest Modulus of Complex Number MCQ Objective Questions

Modulus of Complex Number Question 1:

Comprehension:

Direction : Consider the following for the items that follow :  

Let Z 1  and Z 2  be any two complex numbers such that 

what is the value of 

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

Answer (Detailed Solution Below)

Option 2 : 0

Modulus of Complex Number Question 1 Detailed Solution

Explanation:

∴ Option (b) is correct.

Modulus of Complex Number Question 2:

Comprehension:

Direction : Consider the following for the items that follow :  

Let Z 1  and Z 2  be any two complex numbers such that 

what is the value of ,

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

Modulus of Complex Number Question 2 Detailed Solution

Explanation:

⇒ Z 1  = ω and Z 2  = ω 2

Now

⇒ 

Option (a) is correct.

Modulus of Complex Number Question 3:

If  then what is modulus of Z equal to?  

  1. 1
  2. √2
  3. 2
  4. √3

Answer (Detailed Solution Below)

Option 2 : √2

Modulus of Complex Number Question 3 Detailed Solution

Explanation:

Given

  

|Z| =  √2 

∴ Option (b) is correct.

Modulus of Complex Number Question 4:

If z1 = 1 - 2i, z2 = 1 + i and z3 = 3 + 4i, then 

Answer (Detailed Solution Below)

Option 3 :

Modulus of Complex Number Question 4 Detailed Solution

Concept:

If z = a + ib , |z| = 

If z = a + ib ,  =  

|z1z2| = |z1| × |z2|

Calculation:

Given z1 = 1 - 2i , z2 = 1 + i and z3 = 3 + 4i

∴  =  = 

Similarly   = 2 ×    = 2 ×  = 2 ×   = (1 - i)

 = (1 - i)

⇒ \(\frac{1}{z_{2}} \) = 

 = z×  \(\frac{1}{z_{2}} \)  = (3 + 4i) × 

⇒  =  

 We need to find 

  =  × 

=   × 

 × 

 × 

=  

 

Evaluating , we get .

Modulus of Complex Number Question 5:

If |z| = 4 and arg z = , then z = 

  1.  - 2i
  2.  + 2i
  3.  + 2i
  4.  + i
  5. 2i - √5 

Answer (Detailed Solution Below)

Option 3 : -  + 2i

Modulus of Complex Number Question 5 Detailed Solution

Concept

The general form of a complex number is z = x + iy. The polar representation of z

is z = r(cos θ + i sin θ). Here, r is the modulus of z and θ is called the amplitude or

argument of the complex number. The formula to find the amplitude of a complex

number is:  and ∣z∣ = 

Calculation

Given:

|z| = 4 and arg z = 

Let z = |z| (cos θ + i sin θ) where θ = arg(z)

⇒ z = 

⇒ z = 

⇒ z = - 2√3 + 2i

∴ z = - 2√3 + 2i

Top Modulus of Complex Number MCQ Objective Questions

What is the modulus of  where 

  1. 2√5 
  2. 4
  3. 3
  4. 2

Answer (Detailed Solution Below)

Option 4 : 2

Modulus of Complex Number Question 6 Detailed Solution

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Concept:

Let z = x + iy be a complex number, Where x is called real part of the complex number or Re (z) and y is called Imaginary part of the complex number or Im (z)

Modulus of z = |z| = 

Calculations:

Let 

   

As we know i2 = -1 

As we know that if z = x + iy be any complex number, then its modulus is given by,|z| = 

∴ |z| = 

Find the Modulus of the complex number 

  1. 1/√2
  2. √5 
  3. √3 
  4. √2

Answer (Detailed Solution Below)

Option 1 : 1/√2

Modulus of Complex Number Question 7 Detailed Solution

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Concept;

Modulus of a complex number z = x + iy is given by:

|z| = 

(a + b)(a - b) = a2 - b2

Calculation: 

If z =  so, modulus of |z| = 

z = 

|z| =  

What is the modulus of  where 

  1. 2
  2. 3
  3. 4
  4. 6

Answer (Detailed Solution Below)

Option 1 : 2

Modulus of Complex Number Question 8 Detailed Solution

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Concept:

Let z = x + iy be a complex number, Where x is called the real part of the complex number or Re (z) and y is called the Imaginary part of the complex number or Im (z)

Modulus of z = |z| = 

Calculations:

Let 

z = x + iy = 0 + 2i

As we know that if z = x + iy be any complex number, then its modulus is given by, |z| = 

∴ |z| = 

What is the modulus of the complex number i2n + 1(-i)2n - 1, where n ∈ N and i = √-1?

  1. 1
  2. - 1
  3. √2
  4. 2

Answer (Detailed Solution Below)

Option 1 : 1

Modulus of Complex Number Question 9 Detailed Solution

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Concept:

Iota power:

  • i2 = -1, i3 = -i, i4 = 1, i4n = 1
  • Number of the form 2n is always even, n ∈ N
  • Numebr of the form 2n +1 or 2n - 1 is always odd, n ∈ N
  • (-a)2n -1 = -(a)2n -1

Calculation:

Let,

Z = i2n + 1(-i)2n - 1

⇒ Z = i2n+1 × (i)2n-1 × (-1)2n-1

 Z =  i2n +1+2n-1 ×(-1)2n-1

⇒ Z = i4× (-1)          [∵ (-1)2n-1 = -1]

 Z = (-1)4n ×

 Z = i4n × (-1)

 Z = -(i)4n × (-1)

 Z = 1 × (-1)         [∵ i4n = 1] 

 Z = -1

⇒ |Z| = |-1| = 1

Hence, the modulus of the complex number i2n + 1(-i)2n - 1 is 1.

Find the Modulus of the complex number 

  1. 1

Answer (Detailed Solution Below)

Option 4 :

Modulus of Complex Number Question 10 Detailed Solution

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Concept;

Modulus of a complex number z = x + iy is given by:

|z| = 

(a + b)(a - b) = a2 - b2

Calculation:

Given: z = 

Mutiply by (3 + 4i) in denominator and numerator.

z =  =  =                   (∵ i2 = -1) 

z = 

|z| = 

|z| = √2 

 

If z =  so, modulus of |z| = 

z = 

|z| =  

|z| = √2  

What is the modulus of  (1 + i)2, Where 

  1. 1
  2. 2
  3. -2
  4. 4

Answer (Detailed Solution Below)

Option 2 : 2

Modulus of Complex Number Question 11 Detailed Solution

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Concept:

Let z = x + iy be a complex number, Where x is called real part of the complex number or Re (z) and y is called Imaginary part of the complex number or Im (z)

Modulus of z = |z| = 

Calculations:

Let z = x + iy = (1 + i)2 = 12 + 2i + i2         (∵ (a + b)2 = a2 + b2 + 2ab)

z = 1 + 2i - 1                                (∵ i2 = -1)

∴ z = x + iy = 2i

So, x = 0  and y = 2

As we know that if z = x + iy be any complex number, then its modulus is given by, |z| = 

∴ |z| =  

Find the modulus of z = (1 - i)4 ?

  1. 2
  2. 4
  3. - 4
  4. None of these

Answer (Detailed Solution Below)

Option 2 : 4

Modulus of Complex Number Question 12 Detailed Solution

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CONCEPT:

  • i2 = - 1
  • If z = x + iy then  

CALCULATION:

Given: z = (1 - i)4 First let's simplify the expression (1 - i)4 

⇒ (1 - i)2 = 1 + i2 - 2i

As we know that, i2 = - 1

⇒ (1 + i)2 = -2i

Since (1 - i)(1 - i)× (1 - i)2 we get:

⇒ (1 + i)4 = (-2i)2 = - 4

⇒ z = - 4 + 0i

As we know that, if z = x + iy then  

Here, x = - 4 and y = 0

⇒  

As we know that, |z| denotes the distance between origin and z in the argand plane. So, |z| cannot be negative

⇒ |z| = 4

Hence, correct option is 2.

If z = 2i + 1, find the value of , where  is the conjugate of the complex number z

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 3 : 3

Modulus of Complex Number Question 13 Detailed Solution

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Concept:

The modulus of a complex number z = x + iy

|z| = 

The conjugate  = x - iy

Calculation:

z = 1+ 2i

= 1 - 2i

S = 

S = 

S =  

S = 3

If iz3 + z2 - z + i = 0, then |z| is:

  1. 1
  2. ±1
  3. 0
  4. -1

Answer (Detailed Solution Below)

Option 1 : 1

Modulus of Complex Number Question 14 Detailed Solution

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Concept:

If z = a + ib, then |z| = 

Solution:

The given equation can be solved as:

iz3 + z2 - z + i = 0

⇒ iz3 + i2z + z2 + i = 0

⇒ iz(z2 + i) + (z2 + i) = 0

⇒ (z2 + i)(zi + 1) = 0

⇒ z2 + i = 0 or zi + 1 = 0

⇒ z2 = -i or z = i

|z| = 1 in both the cases.

What is the modulus of the complex number  where  ?

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

Answer (Detailed Solution Below)

Option 1 : 1

Modulus of Complex Number Question 15 Detailed Solution

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Concept: 

Modulus of complex no. z =  a + ib is given by |z| =  . 

Property of complex number:

Calculation:

Let z = 

Taking modulus on both sides, we get

⇒ |z| = 

= 1

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