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**Exercise 5.1 : ** Solutions of Questions on Page Number : **103**

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**Exercise 5.2 : ** Solutions of Questions on Page Number : **108**

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**Exercise 5.3 : ** Solutions of Questions on Page Number : **109**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **112**

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Next Chapter 6 : Linear Inequalities >>
**Popular Articles**

Q1 :
**
**

Express the given complex number in the form *a* +
*ib*:

**Answer :**

Answer needs Correction? Click Here

Q2 :
**
**

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

**Answer :**

Answer needs Correction? Click Here

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

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

**Answer :**

Q5 :
**
**

Express the given complex number in the form *a* +
*ib*: (1 - *i*)
- (-1 + *i*6)

**Answer :**

Q6 :
**
**

Express the given complex number in the form *a* +
*ib*:

**Answer :**

Q7 :
**
**

Express the given complex number in the form *a* +
*ib*:

**Answer :**

Q8 :
**
**

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

**Answer :**

Q9 :
**
**

Express the given complex number in the form *a* +
*ib*:

**Answer :**

Q10 :
**
**

Express the given complex number in the form *a* +
*ib*:

**Answer :**

Q11 :
**
**

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

**Answer :**

Q12 :
**
**

Find the multiplicative inverse of the complex number

**Answer :**

Q13 :
**
**

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

**Answer :**

Q14 :
**
**

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

**Answer :**

Q1 :
**
**

Find the modulus and the argument of the complex number

**Answer :**

Q2 :
**
**

Find the modulus and the argument of the complex number

**Answer :**

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

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

**Answer :**

Q5 :
**
**

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

**Answer :**

Q6 :
**
**

Convert the given complex number in polar form: -3

**Answer :**

Q7 :
**
**

Convert the given complex number in polar form:

**Answer :**

Q8 :
**
**

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

**Answer :**

Q1 :
**
**

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

**Answer :**

Q2 :
**
**

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

**Answer :**

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

Solve the equation -*x*^{2} +
*x* - 2 = 0

**Answer :**

Q5 :
**
**

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

**Answer :**

Q6 :
**
**

Solve the equation *x*^{2} -
*x* + 2 = 0

**Answer :**

Q7 :
**
**

Solve the equation

**Answer :**

Q8 :
**
**

Solve the equation

**Answer :**

Q9 :
**
**

Solve the equation

**Answer :**

Q10 :
**
**

Solve the equation

**Answer :**

Q2 :
**
**

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}

**Answer :**

Q3 :
**
**

Reduce to the standard form.

**Answer :**

Q4 :
**
**

If *x* â€“ *iy* =prove that.

**Answer :**

Q5 :
**
**

Convert the following in the polar form:

(i) , (ii)

**Answer :**

Q6 :
**
**

Solve the equation

**Answer :**

Q7 :
**
**

Solve the equation

**Answer :**

Q8 :
**
**

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

**Answer :**

Q9 :
**
**

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

**Answer :**

Q12 :
**
**

If *a* + *ib* =, prove that
*a*^{2} + *b*^{2} =

**Answer :**

Q13 :
**
**

Let . Find

(i) , (ii)

**Answer :**

Q14 :
**
**

Find the modulus and argument of the complex number.

**Answer :**

Q15 :
**
**

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

**Answer :**

Q16 :
**
**

Find the modulus of .

**Answer :**

Q17 :
**
**

If (*x* + *iy*)^{3} = *u* + *iv*,
then show that.

**Answer :**

Q18 :
**
**

If α and ÃŽÂ² are different complex numbers with = 1, then find.

**Answer :**

Q19 :
**
**

Find the number of non-zero integral solutions of the equation.

**Answer :**

Q20 :
**
**

If (*a* + *ib*) (*c* + *id*) (*e* +
*if*) (*g* + *ih*) = A + *i*B, then show that

(*a*^{2} + *b*^{2})
(*c*^{2} + *d*^{2})
(*e*^{2} + *f*^{2})
(*g*^{2} + *h*^{2}) = A^{2} +
B^{2}.

**Answer :**

Q21 :
**
**

If, then find the least
positive integral value of *m*.

**Answer :**

Maths - Maths : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Complex Numbers and Quadratic Equations ** ( Exercise 5.1, 5.2, 5.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Maths : Chapter 3 - Trigonometric Functions Class 11
- Maths : Chapter 4 - Principle of Mathematical Induction Class 11
- Maths : Chapter 2 - Relations and Functions Class 11
- Maths : Chapter 1 - Sets Class 11
- Maths : Chapter 9 - Sequences and Series Class 11
- Maths : Chapter 6 - Linear Inequalities Class 11
- Maths : Chapter 7 - Permutations and Combinations Class 11
- Maths : Chapter 13 - Limits and Derivatives Class 11
- Maths : Chapter 8 - Binomial Theorem Class 11

Exercise 5.1 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |

Question 11 |

Question 12 |

Question 13 |

Question 14 |

Exercise 5.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Exercise 5.3 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |

Question 9 |

Question 10 |