# RD SHARMA Solutions for Class 11-science Maths Chapter 13 - Complex Numbers

Page / Exercise

## Chapter 13 - Complex Numbers Exercise Ex. 13.2

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

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

What is the smallest positive integer n for which

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

Solution 24

Question 1 (i)

Solution 1 (i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 1 (v)

Solution 1 (v)

Question 1 (vi)

Solution 1 (vi)

Question 1 (vii)

Solution 1 (vii)

Question 1 (viii)

Solution 1 (viii)

Question 1 (ix)

Solution 1 (ix)

Question 1 (x)

Solution 1 (x)

Question 1 (xi)

Solution 1 (xi)

Question 1 (xii)

Solution 1 (xii)

Question 2 (i)

Solution 2 (i)

Question 2 (ii)

Solution 2 (ii)

Question 2 (iii)

Solution 2 (iii)

Question 2 (iv)

Solution 2 (iv)

Question 3 (i)

Solution 3 (i)

Question 3 (ii)

Solution 3 (ii)

Question 3 (iii)

Solution 3 (iii)

Question 3 (iv)

Solution 3 (iv)

Question 3 (v)

Solution 3 (v)

Question 3 (vi)

Solution 3 (vi)

Question 4 (i)

Solution 4 (i)

Question 4 (ii)

Solution 4 (ii)

Question 4 (iii)

Solution 4 (iii)

Question 4 (iv)

Solution 4 (iv)

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 16 (i)

Solution 16 (i)

Question 16 (ii)

Solution 16 (ii)

Question 16 (iii)

Solution 16 (iii)

Question 16 (iv)

Solution 16 (iv)

Question 16(v)

Evaluate the following :

Solution 16(v)

Question 25

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

Solution 25

Question 26

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

Solution 26

## Chapter 13 - Complex Numbers Exercise Ex. 13.1

Question 1 (i)

Solution 1 (i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 1 (v)

Solution 1 (v)

Question 1 (vi)

Solution 1 (vi)

Question 1 (vii)

Solution 1 (vii)

Question 1 (viii)

Solution 1 (viii)

Question 2

Solution 2

Question 3 (i)

Solution 3 (i)

Question 3 (ii)

Solution 3 (ii)

Question 3 (iii)

Solution 3 (iii)

Question 3 (iv)

Solution 3 (iv)

Question 3 (v)

Solution 3 (v)

Question 3 (vi)

Solution 3 (vi)

Question 3(vii)

Find the values of the following expressions:

(1 + i)6 + (1 - i)3

Solution 3(vii)

## Chapter 13 - Complex Numbers Exercise Ex. 13.3

Question 1 (i)

Solution 1 (i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 1 (v)

Solution 1 (v)

Question 1 (vi)

Solution 1 (vi)

Question 1 (vii)

Solution 1 (vii)

Question 1 (viii)

Solution 1 (viii)

Question 1 (ix)

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

Solution 1 (ix)

## Chapter 13 - Complex Numbers Exercise Ex. 13.4

Question 1 (i)

Solution 1 (i)

Question 1 (ii)

Solution 1 (ii)

Question 1 (iii)

Solution 1 (iii)

Question 1 (iv)

Solution 1 (iv)

Question 1 (v)

Solution 1 (v)

Question 1 (vi)

Solution 1 (vi)

Question 1 (vii)

Solution 1 (vii)

Question 1 (viii)

Solution 1 (viii)

Question 2

Write (i25)3 in polar form.

Solution 2

Question 3(i)

Express the following complex numbers in the form

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

Solution 3(i)

Question 3(ii)

Express the following complex numbers in the form

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

Solution 3(ii)

Question 3(iii)

Express the following complex numbers in the form

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

Solution 3(iii)

Question 3(iv)

Express the following complex numbers in the form

r (cos q + I sin q):

Solution 3(iv)

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

## 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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