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

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1.

• Complex Numbers and Quadratic Equations Class 11 Ex 5.2
• Complex Numbers and Quadratic Equations Class 11 Ex 5.3

Board	CBSE
Textbook	NCERT
Class	Class 11
Subject	Maths
Chapter	Chapter 5
Chapter Name	Complex Numbers and Quadratic Equations
Exercise	Ex 5.1
Number of Questions Solved	14
Category	NCERT Solutions

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

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.
Ex 5.1 Class 11 Maths Question 1.
\(\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right) \)
Solution.
\(\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right) \)
= -3i² = -3(-1)                    [∵ i² = -1]
= 3 = 3 + 0i

Ex 5.1 Class 11 Maths Question 2.
i⁹+ i¹⁹
Solution.

Ex 5.1 Class 11 Maths Question 3.
i^-39
Solution.

Ex 5.1 Class 11 Maths Question 4.
3(7 + i7) + i(7 + i7)
Solution.
3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i²
= 21 + (21 + 7)i + (-1)7 = 21 – 7 + 28i
= 14 + 28i.

Ex 5.1 Class 11 Maths Question 5.
(1 – i) – (- 1 +i6)
Solution.
(1 – i) – (-1 + i6) = 1 – i + 1 – 6i
= (1 +1) – i(1 + 6)
= 2 – 7i

Ex 5.1 Class 11 Maths Question 6.
\(\left( \frac { 1 }{ 5 } +i\frac { 2 }{ 5 } \right) -\left( 4+i\frac { 5 }{ 2 } \right) \)
Solution.

Ex 5.1 Class 11 Maths Question 7.
\(\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right) \)
Solution.

Ex 5.1 Class 11 Maths Question 8.
(1 -i)⁴
Solution.
(1 -i)⁴ = [(1 – i)²]² = [1 – 2i + i²]²
= [1 – 2i + (-1)]²
= (-2i)² = 4i² = 4(-1) = – 4
= – 4 + 0i

Ex 5.1 Class 11 Maths Question 9.
\({ \left( \frac { 1 }{ 3 } +3i \right) }^{ 3 }\)
Solution.

Ex 5.1 Class 11 Maths Question 10.
\({ \left( -2-\frac { 1 }{ 3 } i \right) }^{ 3 }\)
Solution.

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13.
Ex 5.1 Class 11 Maths Question 11.
4 – 3i
Solution.

Ex 5.1 Class 11 Maths Question 12.
\(\sqrt { 5 } +3i\)
Solution.

Ex 5.1 Class 11 Maths Question 13.
-i
Solution.

Ex 5.1 Class 11 Maths Question 14.
Express the following expression in the form of a + ib:
\(\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) } \)
Solution.
We have, \(\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) } \)

 

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