**Exercise 4.1**

Complex Numbers and Quadratic Equations

**Question and Answers**

**Class 11 – Maths**

Complex Numbers and Quadratic Equations

Class | Class 11 |

Subject | Mathematics |

Chapter Name | Complex Numbers and Quadratic Equations |

Chapter No. | Chapter 4 |

Exercise | Exercise 4.1 |

Category | Class 11 Maths NCERT Solutions |

**Question 1 Express each of the complex number in the form a + ib.**

**(5i) (-3/5i)**

**Answer**

(5i) (-3/5i)

= 5 x (-3/5) x i^{2
}= -3 x -1 [i^{2} = -1]
= 3

(5i) (-3/5i) = 3 + i0

**Question 2 Express the given complex number in the form a + ib**

**i ^{9} + i^{19}**

**Answer**

i^{9} + i^{19} = (i^{2})^{4}. i + (i^{2})^{9}. i

= (-1)^{4} . i + (-1)^{9} .i

= 1 x i + -1 x i

= i – i

= 0

Hence,

i^{9} + i^{19} = 0 + i0

**Question 3 Express the given complex number in the form a + ib**

**i ^{-39}**

**Answer**

i^{−39 }= i ^{−4×9−3
}=(i ^{4})^{−9 }. i^{−3
}=(1)^{−9 }. i^{−}^{3 } [i^{4}=1]

**Question 4 Express the given complex number in the form a + ib**

**3 ( 7 + i 7) + i ( 7 + i 7 )**

**Answer
**

3(7 + i 7) + i (7 + i 7) = 21 +21 i + 7 i+ 7 i

^{2 }=21+28 i+7×(−1) [ i

^{2}=−1] = 14 + 28 i

**Question 5 Express the given complex number in the form a + ib**

**Answer**

**(1 – i ) – (–1 + i 6)
**= (1−i)−(−1+ i 6)

= 1- i + 1 -6 i

2 – 7 i

**Question 6 ****Express the given complex number in the form a + ib**

**Answer**

**Question 7** **Express the given complex number in the form a + ib**

**Answer**

**Question 8** **Express the given complex number in the form a + ib**

**(1 – i ) ^{4}**

**Answer**

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

^{2 }= 4(-1)

= -4

Hence, (1 –

*i*)

^{4}= -4 + 0

*i*

**Question 9** **Express the given complex number in the form a + ib**

**Answer**

**Question 10** **Express the given complex number in the form a + ib**

**Answer**

**Question 11 Find the multiplicative inverse of given complex numbers 4 – 3i**

**Answer**

Let z =4- 3i

z̄= 4 + 3i and | z | ^{2 }= 4^{2}+(−3)^{2 }= 16+9 = 25

Thus, the multiplicative inverse of 4 – 3*i* is given by z^{-1
}Z ^{-1} = z̄ / | z | ^{2
}Z ^{-1} = (4 + 3i) / 25

Z ^{-1} = 4/25 + 3i /25

**Question 12 Find the multiplicative inverse of the complex number √5 + 3 i**

**Answer**

z = √5 + 3i

z̄ = √5 – 3i

| z |^{2} = ( √5 )^{2} + 3^{2
}| z |^{2} = 14

**Question 13 Find the multiplicative inverse of the complex number −i.**

**Answer**

Let z=−i

Then, z̄ = i

| z |^{2} = 1

The multiplicative inverse of the complex number −i

Z ^{-1} = z̄ / | z | ^{2
}Z^{-1} = i / 1

Z^{-1} = 1

**Question ****14 Express the following expression in the form of a + ib :**

**Answer**

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