Contents

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 5 |

Chapter Name |
Complex Numbers and Quadratic Equations |

Exercise |
Ex 5.1, Ex 5.2, Ex 5.3 |

Number of Questions Solved |
32 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

**NCERT Exercises**

### Chapter 5 Complex Numbers and Quadratic Equations Exercise – 5.1

Express each of the complex number given in the Exercises 1 to 10 in the form a + ib.

**Question 1.**

**Solution.**

= -3i^{2} = -3(-1) [∵ i^{2} = -1]

= 3 = 3 + 0i

**Question 2.**

i^{9}+ i^{19}

**Solution.**

**Question 3.**

i^{-39}

**Solution.**

**Question 4.**

3(7 + i7) + i(7 + i7)

**Solution.**

3(7 + i7) + i(7 + i7) = 21 + 21i + 7i + 7i^{2}

= 21 + (21 + 7)i + (-1)7 = 21 – 7 + 28i

= 14 + 28i.

**Question 5.**

(1 – i) – (- 1 +i6)

**Solution.**

(1 – i) – (-1 + i6) = 1 – i + 1 – 6i

= (1 +1) – i(1 + 6)

= 2 – 7i

**Question 6.**

**Solution.**

**Question 7.**

**Solution.**

**Question 8.**

(1 -i)^{4}

**Solution.**

(1 -i)^{4} = [(1 – i)^{2}]^{2} = [1 – 2i + i^{2}]^{2}

= [1 – 2i + (-1)]^{2}

= (-2i)^{2} = 4i^{2} = 4(-1) = – 4

= – 4 + 0i

**Question 9.**

**Solution.**

**Question 10.**

**Solution.**

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

**Question 11.**

4 – 3i

**Solution.**

**Question 12.**

**Solution.**

**Question 13.**

-i

**Solution.**

**Question 14.**

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

**Solution.**

We have,

### Chapter 5 Complex Numbers and Quadratic Equations Exercise – 5.2

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.

**Question 1.**

**Solution.**

We have,

**Question 2.**

**Solution.**

We have,

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

**Question 3.**

1 – i

**Solution.**

We have, z = 1 – i

**Question 4.**

-1 + i

**Solution.**

We have, z = -1 + i

**Question 5.**

-1 – i

**Solution.**

We have, z = -1 – i

**Question 6.**

-3

**Solution.**

We have, z = -3, i.e., z = -3 + 0i

**Question 7.**

**Solution.**

We have,

**Question 8.**

i

**Solution.**

We have, z = i, i.e., z = 0 + 1.i

### Chapter 5 Complex Numbers and Quadratic Equations Exercise – 5.3

Solve each of the following equations:

**Question 1.**

x^{2} + 3 = 0

**Solution.**

We have, x^{2} + 3 = 0 ⇒ x^{2} = -3

⇒ ⇒ x =

**Question 2.**

2x^{2} + x + 1 = 0

**Solution.**

We have, 2x^{2} + x + 1 = 0

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get

**Question 3.**

x^{2} + 3x + 9 = 0

**Solution.**

We have, x^{2} + 3x + 9 = 0

Comparing the given equation with the general form ax^{2} + bx + c = 0,we get a = 1, b = 3, c = 9

**Question 4.**

-x^{2} + x – 2 = 0

**Solution.**

We have, -x^{2} + x – 2 = 0

Comparing the given equation with the general form ax^{2} + bx + c = 0,we get

a = 1, b = 1, c = -2

**Question 5.**

x^{2} + 3x + 5 = 0

**Solution.**

We have, x^{2} + 3x + 5 = 0

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get a = 1, b = 3, c = 5.

**Question 6.**

x^{2} – x + 2 = 0

**Solution.**

We have, x^{2} – x + 2 = 0

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get a = 1, b = -1, c = 2.

**Question 7.**

**Solution.**

We have,

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get

**Question 8.**

**Solution.**

We have,

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get

**Question 9.**

**Solution.**

We have,

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get

**Question 10.**

**Solution.**

We have,

Comparing the given equation with the general form ax^{2} + bx + c = 0, we get

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