#### Online Mock Tests

#### Chapters

Chapter 2: Relations and Functions

Chapter 3: Trigonometric Functions

Chapter 4: Principle of Mathematical Induction

▶ Chapter 5: Complex Numbers and Quadratic Equations

Chapter 6: Linear Inequalities

Chapter 7: Permutations and Combinations

Chapter 8: Binomial Theorem

Chapter 9: Sequences and Series

Chapter 10: Straight Lines

Chapter 11: Conic Sections

Chapter 12: Introduction to Three Dimensional Geometry

Chapter 13: Limits and Derivatives

Chapter 14: Mathematical Reasoning

Chapter 15: Statistics

Chapter 16: Probability

## 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.

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

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

Express the given complex number in the form a + ib: i^{9} + i^{19}

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

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

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

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

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

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

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

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

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

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

Find the multiplicative inverse of the complex number –*i*

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

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

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

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

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

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

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

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

Convert the given complex number in polar form: –3

Convert the given complex number in polar form `sqrt3 + i`

Convert the given complex number in polar form: *i*

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

Solve the equation x^{2} + 3 = 0

Solve the equation 2x^{2} + x + 1 = 0

Solve the equation x^{2} + 3x + 9 = 0

Solve the equation –x^{2} + x – 2 = 0

Solve the equation x^{2} + 3x + 5 = 0

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

Solve the equation x^{2} – x + 2 = 0

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

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

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

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

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

For any two complex numbers_{ }z_{1} and z_{2}, prove that Re (z_{1}z_{2})_{ }= Re z_{1 }Re z_{2} – Im z_{1} Im z_{2}

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

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

Convert the following in the polar form:

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

Convert the following in the polar form:

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

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

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

Solve the equation 27x^{2} – 10x + 1 = 0

Solve the equation 21x^{2} – 28x + 10 = 0

If z_{1} = 2 – i, z_{2} = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`

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

Let z_{1} = 2 – i, z_{2} = –2 + i. Find Re`((z_1z_2)/barz_1)`

Let z_{1} = 2 – i, z_{2} = –2 + i. Find `Im(1/(z_1barz_1))`

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

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

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

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

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

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

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a^{2} + b^{2}) (c^{2} + d^{2}) (e^{2} + f^{2}) (g^{2} + h^{2}) = A^{2} + B^{2}.

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

## 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.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

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.

Using NCERT Class 11 Mathematics solutions Complex Numbers and Quadratic Equations exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Class 11 Mathematics students prefer NCERT Textbook Solutions to score more in exams.

Get the free view of Chapter 5, Complex Numbers and Quadratic Equations Class 11 Mathematics additional questions for Mathematics Class 11 Mathematics CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.