NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1 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 Ex 5.1.

- Complex Numbers and Quadratic Equations Class 11 Ex 5.2
- Complex Numbers and Quadratic Equations Class 11 Ex 5.3

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 5 |

Chapter Name |
Complex Numbers and Quadratic Equations |

Exercise |
Ex 5.1 |

Number of Questions Solved |
14 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.1

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

**Ex 5.1 Class 11 Maths Question 1.**

\(\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right) \)

**Solution.**

\(\left( 5i \right) \left( -\frac { 3 }{ 5 } i \right) \)

= -3i^{2} = -3(-1) [∵ i^{2} = -1]

= 3 = 3 + 0i

**Ex 5.1 Class 11 Maths Question 2.**

i^{9}+ i^{19}

**Solution.**

**Ex 5.1 Class 11 Maths Question 3.**

i^{-39}

**Solution.**

**Ex 5.1 Class 11 Maths 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.

**Ex 5.1 Class 11 Maths Question 5.**

(1 – i) – (- 1 +i6)

**Solution.**

(1 – i) – (-1 + i6) = 1 – i + 1 – 6i

= (1 +1) – i(1 + 6)

= 2 – 7i

**Ex 5.1 Class 11 Maths Question 6.**

\(\left( \frac { 1 }{ 5 } +i\frac { 2 }{ 5 } \right) -\left( 4+i\frac { 5 }{ 2 } \right) \)

**Solution.**

**Ex 5.1 Class 11 Maths Question 7.**

\(\left[ \left( \frac { 1 }{ 3 } +i\frac { 7 }{ 3 } \right) +\left( 4+i\frac { 1 }{ 3 } \right) \right] -\left( -\frac { 4 }{ 3 } +i \right) \)

**Solution.**

**Ex 5.1 Class 11 Maths 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

**Ex 5.1 Class 11 Maths Question 9.**

\({ \left( \frac { 1 }{ 3 } +3i \right) }^{ 3 }\)

**Solution.**

**Ex 5.1 Class 11 Maths Question 10.**

\({ \left( -2-\frac { 1 }{ 3 } i \right) }^{ 3 }\)

**Solution.**

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

**Ex 5.1 Class 11 Maths Question 11.**

4 – 3i

**Solution.**

**Ex 5.1 Class 11 Maths Question 12.**

\(\sqrt { 5 } +3i\)

**Solution.**

**Ex 5.1 Class 11 Maths Question 13.**

-i

**Solution.**

**Ex 5.1 Class 11 Maths Question 14.**

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

\(\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) } \)

**Solution.**

We have, \(\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) } \)

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