#### 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

## Chapter 5: Complex Numbers and Quadratic Equations

### 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*.

## Chapter 5: Complex Numbers and Quadratic Equations

## 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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