# RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3

## Rajasthan Board RBSE Class 11 Maths Chapter 5 Complex Numbers Ex 5.3

Question 1.
Find the square root of the following complex numbers:
(i) -5 + 12i
(ii) 8 – 6i
(iii) -i
Solution:
Formula

Question 2.
Find the value of $$\sqrt { 4+3\sqrt { -20 } } +\sqrt { 4-3\sqrt { -20 } }$$
Solution:
From formula $$\sqrt { a+ib }$$ =

Question 3.
Find the cube root of the following:
(i) -216
(ii) -512
Solution:
(i) -216 = (-6) (1)1/3 = -6, -6ω, -6ω2
Hence, cube root of -216 = -6, -6ω, -6ω2
(ii) -512 = (-8) (1)1/3 = -8, -8ω, -8ω2
Hence, cube root of -512 = -8, -8ω, – 8ω2

Question 4.
Prove that:
(i) 1 + ωn + ω2n = 0, whereas n = 2, 4
(ii) 1 + ωn + ω2n = 3, whereas n is multiple of 3.
Solution:

Question 5.
Prove that:

(ii) (1 + 5ω2 + ω) (1 + 5ω + ω2) (5 + ω + ω2) = 64
Solution:
(i) ω is cube root of unity.