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

May 28, 2019 by Prasanna Leave a Comment

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
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 1
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 2
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 3

Question 2.
Find the value of \sqrt { 4+3\sqrt { -20 } } +\sqrt { 4-3\sqrt { -20 } }
Solution:
From formula \sqrt { a+ib } =
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 4

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

Question 5.
Prove that:
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 6
(ii) (1 + 5ω2 + ω) (1 + 5ω + ω2) (5 + ω + ω2) = 64
Solution:
(i) ω is cube root of unity.
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 7
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers Ex 5.3 8

RBSE Solutions for Class 11 Maths

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