NCERT Solutions for Exercise 4.1, Class 11, Maths

Exercise 4.1
Complex Numbers and Quadratic Equations
Question and Answers
Class 11 – Maths

Class	Class 11
Subject	Mathematics
Chapter Name	Complex Numbers and Quadratic Equations
Chapter No.	Chapter 4
Exercise	Exercise 4.1
Category	Class 11 Maths NCERT Solutions

Question 1 Express each of the complex number in the form a + ib.

(5i) (-3/5i)

Answer

(5i) (-3/5i)
= 5 x (-3/5) x i²
= -3 x -1       [i² = -1] = 3
(5i) (-3/5i) = 3 + i0

Question 2 Express the given complex number in the form a + ib

i⁹ + i¹⁹

Answer

i⁹ + i¹⁹ = (i²)⁴. i + (i²)⁹. i
= (-1)⁴ . i + (-1)⁹ .i
= 1 x i + -1 x i
= i – i
= 0
Hence,
i⁹ + i¹⁹ = 0 + i0

Question 3 Express the given complex number in the form a + ib

i^-39

Answer

i⁻³⁹ = i ^−4×9−3
=(i ⁴)⁻⁹ . i⁻³
=(1)⁻⁹ . i⁻³         [i⁴=1]

Question 4 Express the given complex number in the form a + ib

3 ( 7 + i 7) + i ( 7 + i 7 )

Answer

3(7 + i 7) + i (7 + i 7) =  21 +21 i + 7 i+ 7 i²
=21+28 i+7×(−1)       [ i²=−1] = 14 + 28 i

Question 5 Express the given complex number in the form a + ib

Answer

(1 – i ) – (–1 + i 6)
= (1−i)−(−1+ i 6)
= 1- i + 1 -6 i
2 – 7 i

Question 6 Express the given complex number in the form a + ib

Answer

Question 7 Express the given complex number in the form a + ib

Answer

Question 8 Express the given complex number in the form a + ib

(1 – i )⁴

Answer

(1 – i) ⁴ = [(1 – i)²]²
= [1 + i² – 2i]²
= [1 – 1 – 2i]² [i² = -1] = (-2i)²
= 4(-1)
= -4
Hence, (1 – i)⁴ = -4 + 0i

Question 9 Express the given complex number in the form a + ib

Answer

Question 10 Express the given complex number in the form a + ib

Answer

Question 11 Find the multiplicative inverse of given complex numbers  4 – 3i

Answer

Let z =4- 3i
z̄= 4 + 3i and | z | ² = 4²+(−3)² = 16+9 = 25
Thus, the multiplicative inverse of 4 – 3i is given by z^-1
Z ^-1 = z̄ / | z | ²
Z ^-1 = (4 + 3i) / 25
Z ^-1 = 4/25 + 3i /25

Answer

z = √5 + 3i
z̄ = √5 – 3i
| z |² = ( √5 )² + 3²
| z |² = 14

Question 13 Find the multiplicative inverse of the complex number −i.

Answer

Let z=−i
Then, z̄ =  i
| z |² = 1
The multiplicative inverse of the complex number −i
Z ^-1 = z̄ / | z | ²
Z^-1 = i / 1
Z^-1 = 1

Question 14  Express the following expression in the form of a + ib :

Answer