RD SHARMA SOLUTION CHAPTER- 13 Complex Numbers I CLASS 11TH MATHEMATICS-EDUGROW

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)³Solution 3(vii)

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 = 0Solution 26

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: -iSolution 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 – iSolution 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