# RD Sharma Solution Class 11 Mathematics Chapter 13 Complex Numbers

## Chapter 13 – Complex Numbers Exercise Ex. 13.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Find the values of the following expressions:

(1 + i)6 + (1 – i)3

Solution 16

## Chapter 13 – Complex Numbers Exercise Ex. 13.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Evaluate the following :

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 48

Solution 48

Question 49

Solution 49

Question 50

What is the smallest positive integer n for which

(1+i)2n = (1-i)2n?

Solution 50

Question 51

If z1, z2, z3 are
complex numbers such that |z1| = |z2| = |z3|
=  = 1, then
find the value of |z1 + z2 + z3|.

Solution 51

Question 52

Find the number of solutions of z2 + |z|2
= 0

Solution 52

## Chapter 13 – Complex Numbers Exercise Ex. 13.3

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Find the square root of the following complex numbers: -i

Solution 9

## Chapter 13 – Complex Numbers Exercise Ex. 13.4

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Write (i25)3 in polar form.

Solution 9

Question 10

Express the following complex numbers in the form

r(cos q + I sin q): 1 + i tan a

Solution 10

Question 11

Express the following complex numbers in the form

r(cos q + I sin q): tan ai

Solution 11

Question 12

Express the following complex numbers in the form

r (cos q + I sin q): 1 – sin a + i cos a

Solution 12

Question 13

Express the following complex numbers in the form

r (cos q + I sin q):

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

## Chapter 13 – Complex Numbers Exercise Ex. 13VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

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