# NCERT solutions for Class 11 Mathematics chapter 5 - Complex Numbers and Quadratic Equations [Latest edition]

#### Chapters ## Chapter 5: Complex Numbers and Quadratic Equations

Exercise 5.1Exercise 5.2Exercise 5.3Miscellaneous Exercise
Exercise 5.1 [Pages 103 - 104]

### NCERT solutions for Class 11 Mathematics Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.1 [Pages 103 - 104]

Exercise 5.1 | Q 1 | Page 103

Express the given complex number in the form a + ib: (5i) (- 3/5 i)

Exercise 5.1 | Q 2 | Page 103

Express the given complex number in the form a + ib: i9 + i19

Exercise 5.1 | Q 3 | Page 103

Express the given complex number in the form a + ib: i–39

Exercise 5.1 | Q 4 | Page 104

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Exercise 5.1 | Q 5 | Page 104

Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)

Exercise 5.1 | Q 6 | Page 104

Express the given complex number in the form a + ib: (1/5 + i 2/5) - (4 + i 5/2)

Exercise 5.1 | Q 7 | Page 104

Express the given complex number in the form a + ib : [(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)

Exercise 5.1 | Q 8 | Page 104

Express the given complex number in the form a + ib:  (1 – i)4

Exercise 5.1 | Q 9 | Page 104

Express the given complex number in the form a + ib: (1/3 + 3i)^3

Exercise 5.1 | Q 10 | Page 104

Express the given complex number in the form a + ib: (-2 - 1/3 i)^3

Exercise 5.1 | Q 11 | Page 104

Find the multiplicative inverse of the complex number 4 – 3i

Exercise 5.1 | Q 12 | Page 104

Find the multiplicative inverse of the complex number sqrt5 + 3i

Exercise 5.1 | Q 13 | Page 104

Find the multiplicative inverse of the complex number –i

Exercise 5.1 | Q 14 | Page 104

Express the following expression in the form of a + ib.

((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))

Exercise 5.2 [Page 108]

### NCERT solutions for Class 11 Mathematics Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.2 [Page 108]

Exercise 5.2 | Q 1 | Page 108

Find the modulus and the argument of the complex number  z = – 1 – isqrt3

Exercise 5.2 | Q 2 | Page 108

Find the modulus and the argument of the complex number z =- sqrt3 + i

Exercise 5.2 | Q 3 | Page 108

Convert the given complex number in polar form: 1 – i

Exercise 5.2 | Q 4 | Page 108

Convert the given complex number in polar form: – 1 + i

Exercise 5.2 | Q 5 | Page 108

Convert the given complex number in polar form: – 1 – i

Exercise 5.2 | Q 6 | Page 108

Convert the given complex number in polar form: –3

Exercise 5.2 | Q 7 | Page 108

Convert the given complex number in polar form sqrt3 + i

Exercise 5.2 | Q 8 | Page 108

Convert the given complex number in polar form: i

Exercise 5.3 [Page 109]

### NCERT solutions for Class 11 Mathematics Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.3 [Page 109]

Exercise 5.3 | Q 1 | Page 109

Solve the equation x2 + 3 = 0

Exercise 5.3 | Q 2 | Page 109

Solve the equation 2x2 + x + 1 = 0

Exercise 5.3 | Q 3 | Page 109

Solve the equation x2 + 3x + 9 = 0

Exercise 5.3 | Q 4 | Page 109

Solve the equation –x2 + x – 2 = 0

Exercise 5.3 | Q 5 | Page 109

Solve the equation x2 + 3x + 5 = 0

Exercise 5.3 | Q 5.3 | Page 109

Solve the equation x^2 + x + 1/sqrt2 = 0

Exercise 5.3 | Q 6 | Page 109

Solve the equation x2 – x + 2 = 0

Exercise 5.3 | Q 7 | Page 109

Solve the equation  sqrt2x^2 + x + sqrt2 = 0

Exercise 5.3 | Q 8 | Page 109

Solve the equation  sqrt3 x^2 - sqrt2x + 3sqrt3 = 0

Exercise 5.3 | Q 10 | Page 109

Solve the equation  x^2 + x/sqrt2 + 1 = 0

Miscellaneous Exercise [Pages 112 - 113]

### NCERT solutions for Class 11 Mathematics Chapter 5 Complex Numbers and Quadratic Equations Miscellaneous Exercise [Pages 112 - 113]

Miscellaneous Exercise | Q 1 | Page 112

Evaluate : [i^18 + (1/i)^25]^3

Miscellaneous Exercise | Q 2 | Page 112

For any two complex numbers z1 and z2, prove that Re (z1z2) = Re zRe z2 – Im z1 Im z2

Miscellaneous Exercise | Q 3 | Page 112

Reduce  (1/(1-4i) - 2/(1+i))((3-4i)/(5+i)) to the standard form.

Miscellaneous Exercise | Q 4 | Page 112

If x – iy = sqrt((a-ib)/(c - id)) prove that (x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)

Miscellaneous Exercise | Q 5.1 | Page 112

Convert the following in the polar form:

(1+7i)/(2-i)^2

Miscellaneous Exercise | Q 5.2 | Page 112

Convert the following in the polar form:

(1+3i)/(1-2i)

Miscellaneous Exercise | Q 6 | Page 112

Solve the equation 3x^2 - 4x + 20/3 = 0

Miscellaneous Exercise | Q 7 | Page 112

Solve the equation   x^2 -2x + 3/2 = 0

Miscellaneous Exercise | Q 8 | Page 112

Solve the equation 27x2 – 10x + 1 = 0

Miscellaneous Exercise | Q 9 | Page 113

Solve the equation 21x2 – 28x + 10 = 0

Miscellaneous Exercise | Q 10 | Page 113

If z1 = 2 – i,  z2 = 1 + i, find |(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|

Miscellaneous Exercise | Q 11 | Page 113

If a + ib  = (x + i)^2/(2x^2 + 1) prove that a2 + b= (x^2 + 1)^2/(2x + 1)^2

Miscellaneous Exercise | Q 12.1 | Page 113

Let z1 = 2 – i, z2 = –2 + i. Find Re((z_1z_2)/barz_1)

Miscellaneous Exercise | Q 12.2 | Page 113

Let z1 = 2 – i, z2 = –2 + i. Find Im(1/(z_1barz_1))

Miscellaneous Exercise | Q 13 | Page 113

Find the modulus and argument of the complex number (1 + 2i)/(1-3i)

Miscellaneous Exercise | Q 14 | Page 113

Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

Miscellaneous Exercise | Q 15 | Page 113

Find the modulus  of  (1+i)/(1-i) - (1-i)/(1+i)

Miscellaneous Exercise | Q 16 | Page 113

If (x + iy)3 = u + iv, then show that u/x + v/y  =4(x^2 - y^2)

Miscellaneous Exercise | Q 17 | Page 113

If α and β are different complex numbers with |β| = 1, then find |(beta - alpha)/(1-baralphabeta)|

Miscellaneous Exercise | Q 18 | Page 113

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

Miscellaneous Exercise | Q 19 | Page 113

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.

Miscellaneous Exercise | Q 20 | Page 113

if ((1+i)/(1-i))^m =   1, then find the least positive integral value of m.

## Chapter 5: Complex Numbers and Quadratic Equations

Exercise 5.1Exercise 5.2Exercise 5.3Miscellaneous Exercise ## NCERT solutions for Class 11 Mathematics chapter 5 - Complex Numbers and Quadratic Equations

NCERT solutions for Class 11 Mathematics chapter 5 (Complex Numbers and Quadratic Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics chapter 5 Complex Numbers and Quadratic Equations are Argand Plane and Polar Representation, Quadratic Equations, Algebra of Complex Numbers - Equality, Algebraic Properties of Complex Numbers, Need for Complex Numbers, Square Root of a Complex Number, Algebra of Complex Numbers, The Modulus and the Conjugate of a Complex Number, Concept of Complex Numbers.

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