## EXERCISE 5.1

#### Page No 103:

#### Question 1:

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

#### Answer:

#### Question 2:

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

#### Answer:

#### Question 3:

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

#### Answer:

#### Page No 104:

#### Question 4:

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

#### Answer:

#### Question 5:

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

#### Answer:

#### 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:

#### 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 the complex number 4 – 3*i*

#### Answer:

Let *z* = 4 – 3*i*

Then,

= 4 + 3*i *and

Therefore, the multiplicative inverse of 4 – 3*i* is given by

#### Question 12:

Find the multiplicative inverse of the complex number

#### Answer:

Let *z* =

Therefore, the multiplicative inverse ofis given by

#### Question 13:

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

#### Answer:

Let *z* = –*i*

Therefore, the multiplicative inverse of –*i* is given by

#### Question 14:

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

#### Answer: