NCERT Grade 11-Complex Numbers and Quadratic Equations-Questions

NCERT Solutions for Class 11 Maths

Find 100% accurate solutions for NCERT Class XI Maths. All questions have been explained and solved step-by-step, to help you understand thoroughly. Free Download option available!

Sign Up to Download as PDF

Complex Numbers and Quadratic Equations

Exercise 1

1.     

2.     i9 + i19

3.      i-39

4.     3(7 + i7) + i(7 + i7)

5.     (1 – i) – (-1 + i6)

6.   

7.     

8.    (1 – i)4

9.   

10.   

Find the multiplicative inverse of each of the complex numbers given in the exercises 11 to 13.

11.   4 – 3i

12.   √5 + 3i

13.   -i

14.   Express the following expression in the form of 

Exercise 2

Find the modulus and the argument of each of the complex numbers in exercise 1 to 2.

15.   z = -1 – i√3

16.   z = -√3 + i

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form.

17.   1 – i

18.   -1 + i

19.   -1 -i

20.   -3

21.   √3 + i

22.   i

Exercise 3

Solve each of the following equations:

23.   x2 + 3 = 0

24.   2x2 + x + 1 = 0

25.   x2 + 3x + 9 = 0

26.   -x2 + x – 2 = 0

27.   x2 + 3x + 5 = 0

28.   x2 – x + 2 = 0

29.   √2x2 + x + √2 = 0

30.   √3x2 – √2x + 3√3 = 0

31.   

32.   

Exercise 4

33.    

34.   For any two complex numbers z1 and z2 prove that Re(z1z2) = Rez1Rez2 – Im z1 Im z2

35.   Reduce  to the standard form.

36.   If   prove that 

37.   Convert the following in the polar form:

Solve each of the equations in exercises 6 to 9:

38.   

39.   

40.   27x2 – 10x + 1 = 0

41.   21x2 – 28x + 10 = 0

42.   

43.   

44.   Let z1 = 2 – i, z2 = -2 + i find:

45.   Find the modulus and argument of the complex number 

46.   Find the real numbers x and y if (x-iy) (x+5i) is the conjugate of -6-24i.

47.   Find the modulus of 

48.   If (x + iy)3 = u + iv, then show that 

49.   If α and β are different complex numbers with |β| = 1 then find 

50.   Find the number of non-zero integral solutions of the equation |1 – i|x = 2x.

51.   If (a + ib) (c + id) (e + if) (g + ih) = A + iB then show that:

(a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.

52.   If  then find the least positive integral value of m.

MySchoolPage connects you with exceptional, certified math tutors who help you stay focused, understand concepts better and score well in exams!

Have a Question?




Mathematics - Videos


Physics - Videos


Biology - Videos


Chemistry - Videos