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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 5 |

Exercise | Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.1 |

Number of Questions Solved | 14 |

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

**NCERT TEXTBOOK EXERCISES**

**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) [âˆµ 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 â€“ 7 + 28i

= 14 + 28i.

**Ex 5.1 Class 11 Maths Question 5. (1 â€“ i) â€“ (- 1 +i6)**

**Solution.**

(1 â€“ i) â€“ (-1 + i6) = 1 â€“ i + 1 â€“ 6i

= (1 +1) â€“ i(1 + 6)

= 2 â€“ 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 â€“ i)^{2}]^{2} = [1 â€“ 2i + i^{2}]^{2}

= [1 â€“ 2i + (-1)]^{2}

= (-2i)^{2} = 4i^{2} = 4(-1) = â€“ 4

= â€“ 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 â€“ 3i**

**Solution.**

**Ex 5.1 Class 11 Maths Question 12. âˆš5+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, $\frac { \left( 3+i\sqrt { 5 } \right) \left( 3-i\sqrt { 5 } \right) }{ \left( \sqrt { 3 } +\sqrt { 2 } i \right) -\left( \sqrt { 3 } -i\sqrt { 2 } \right) }$

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

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