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

Chapter 13 - Complex Numbers Exercise Ex. 13.2

Question 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 12

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 13

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 14

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 15

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 17

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 18

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 19

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 20

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 20

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 21

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 22

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 23

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 24

What is the smallest positive integer n for which

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

Solution 24

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (ix)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (ix)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (x)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (x)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (xi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (xi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (xii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (xii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 2 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 2 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 2 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 2 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 4 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 4 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 4 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 4 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 4 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 4 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 4 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 4 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers
Question 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 11

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 16 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 16 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 16 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 16 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 16 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 16 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 16 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 16 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 16(v)

Evaluate the following :

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Solution 16(v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Question 25

If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers = 1, then find the value of |z1 + z2 + z3|.

Solution 25

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Question 26

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

Solution 26

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Chapter 13 - Complex Numbers Exercise Ex. 13.1

Question 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3(vii)

Find the values of the following expressions:

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

Solution 3(vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Chapter 13 - Complex Numbers Exercise Ex. 13.3

Question 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (ix)

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

Solution 1 (ix)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Chapter 13 - Complex Numbers Exercise Ex. 13.4

Question 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (v)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vi)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (vii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1 (viii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2

Write (i25)3 in polar form.

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3(i)

Express the following complex numbers in the form

 r(cos q + I sin q): 1 + i tan a 

Solution 3(i)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Question 3(ii)

Express the following complex numbers in the form

 r(cos q + I sin q): tan a - i

Solution 3(ii)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

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)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

 

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

 

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

 

Question 3(iv)

Express the following complex numbers in the form

 r (cos q + I sin q):Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3(iv)

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers 

Question 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Chapter 13 - Complex Numbers Exercise Ex. 13VSAQ

Question 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 1

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 2

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 3

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 4

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 5

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 6

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 7

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 8

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 9

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Question 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers

Solution 10

Rd-sharma Solutions Cbse Class 11-science Mathematics Chapter - Complex Numbers