Class 11 Maths NCERT Solutions for Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.1

1. Express the given complex number in the form a + ib: (5i) (-3/5)i

Solution

(5i) (-3/5)i = -5 × (3/5) × i × i
= -3i²
= -3(-1) [i² = -1]
= 3

2. Express the given complex number in the form a + ib : i⁹ + i¹⁹

Solution

i⁹ + i¹⁹ = i^4×2+1 + i^4×4+3
= (i⁴)². i + (i⁴)⁴. i³
= 1×i + 1×(-i) [i⁴ = 1, i³ = -i]
= i + (-i)
= 0

3. Express the given complex number in the form a +ib : i^-39

Solution

4. Express the given complex number in the form a + ib : 3(7 + i7) + i(7 + i7)

Solution

3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i²
= 21 + 28i + 7 × (-1) [∵i² = -1]
= 14 + 28i

5. Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

Solution

(1 - i) - (-1 + i6) = 1 - i + 1 - 6i
= 2 - 7i

6. Express the given complex number in the form a + ib: (1/5 +i 2/5) - (4 + i 5/2)

Solution

7. Express the given complex number in the form a + ib: [(1/3 + i 7/3) + (4 + i 1/3)] - (-4/3 + i)

Solution

8. Express the given complex number in the form a + ib : (1 - i )⁴

Solution

(1 -i)² = [(1 - i)²]²
= [1² + i² + 2i²]²
= [1 - 1 - 2i]²
= (-2i)²
= (-2i)×(-2i)
= 4i² = -4 [i²  = -1]

9. Express the given complex number in the form a + ib : (1/3 + 3i)³

Solution

10. Express the given complex number in the form a + ib : [-2 - (1/3)i]³

Solution

11. Find the multiplicative inverse of the complex number 4 - 3i

Solution

Let z = 4 - 3i
Then, z = 4 + 3i and |z|² = 4² + (-3)² = 16 + 9 = 25
Therefore, the multiplicative inverse of 4 - 3i is given by

12. Find the multiplicative inverse of the complex number √5 + 3i

Solution

Let z = √5 + 3i
Then, z = √5 + 3i and |z|² = (√5)² + 3² = 5 + 9= 14
Therefore, the multiplicative inverse of √5 + 3i is given by

13. Find the multiplicative inverse of the complex number –i

Solution

Let z = -i
Then, z = i and |z|² = 1² = 1
Therefore, the multiplicative inverse of -i is given by

z^-1 = z /|z|² = i/1 = i

14. Express the following expression in the form of a + ib.
[(3 + i√5)(3 - i√5)]/[(√3 + √2i)- (√3 - i√2)]

Solution

NCERT Solutions For Class 11 Math Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.1