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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
Modulus of Complex Number Question 3 Detailed Solution
Explanation:
Given
|Z| =
∴ 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)
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
⇒ \(\frac{1}{z_{2}} \) =
⇒
We need to find
=
=
=
=
=
=
=
=
=
Evaluating , we get
Modulus of Complex Number Question 5:
If |z| = 4 and arg z =
Answer (Detailed Solution Below)
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:
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
Answer (Detailed Solution Below)
Modulus of Complex Number Question 6 Detailed Solution
Download Solution PDFConcept:
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
Answer (Detailed Solution Below)
Modulus of Complex Number Question 7 Detailed Solution
Download Solution PDFConcept;
Modulus of a complex number z = x + iy is given by:
|z| =
(a + b)(a - b) = a2 - b2
Calculation:
If z =
z =
|z| =
What is the modulus of
Answer (Detailed Solution Below)
Modulus of Complex Number Question 8 Detailed Solution
Download Solution PDFConcept:
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?
Answer (Detailed Solution Below)
Modulus of Complex Number Question 9 Detailed Solution
Download Solution PDFConcept:
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 = i4n × (-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
Answer (Detailed Solution Below)
Modulus of Complex Number Question 10 Detailed Solution
Download Solution PDFConcept;
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 =
z =
|z| =
|z| = √2
If z =
z =
|z| =
|z| = √2
What is the modulus of (1 + i)2, Where
Answer (Detailed Solution Below)
Modulus of Complex Number Question 11 Detailed Solution
Download Solution PDFConcept:
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 ?
Answer (Detailed Solution Below)
Modulus of Complex Number Question 12 Detailed Solution
Download Solution PDFCONCEPT:
- 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)4 = (1 - i)2 × (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
Answer (Detailed Solution Below)
Modulus of Complex Number Question 13 Detailed Solution
Download Solution PDFConcept:
The modulus of a complex number z = x + iy
|z| =
The conjugate
Calculation:
z = 1+ 2i
S =
S =
S =
S = 3
If iz3 + z2 - z + i = 0, then |z| is:
Answer (Detailed Solution Below)
Modulus of Complex Number Question 14 Detailed Solution
Download Solution PDFConcept:
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
Answer (Detailed Solution Below)
Modulus of Complex Number Question 15 Detailed Solution
Download Solution PDFConcept:
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