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

## Solutions for Chapter 5: Complex Numbers and Quadratic Equations

Below listed, you can find solutions for Chapter 5 of CBSE, Karnataka Board PUC NCERT for Class 11 Mathematics.

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.

## Solutions for 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

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC 5 (Complex Numbers and Quadratic Equations) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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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, Algebraic Operations of Complex Numbers, The Modulus and the Conjugate of a Complex Number, Concept of Complex Numbers.

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