## EXERCISE 5.2

#### Page No 108:

#### Question 1:

Find the modulus and the argument of the complex number

#### Answer:

On squaring and adding, we obtain

Since both the values of sin *θ* and cos *θ* are negative and sin*θ* and cos*θ* are negative in III quadrant,

Thus, the modulus and argument of the complex number are 2 and respectively.

#### Question 2:

Find the modulus and the argument of the complex number

#### Answer:

On squaring and adding, we obtain

Thus, the modulus and argument of the complex number are 2 and respectively.

#### Question 3:

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

#### Answer:

1 – *i*

Let *r* cos *θ* = 1 and *r* sin *θ* = –1

On squaring and adding, we obtain

This is the required polar form.

#### Question 4:

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

#### Answer:

– 1 + *i*

Let *r* cos *θ* = –1 and *r* sin *θ* = 1

On squaring and adding, we obtain

It can be written,

This is the required polar form.

#### Question 5:

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

#### Answer:

– 1 – *i*

Let *r* cos *θ* = –1 and *r* sin *θ* = –1

On squaring and adding, we obtain

This is the required polar form.

#### Question 6:

Convert the given complex number in polar form: –3

#### Answer:

–3

Let *r* cos *θ* = –3 and *r* sin *θ* = 0

On squaring and adding, we obtain

This is the required polar form.

#### Question 7:

Convert the given complex number in polar form:

#### Answer:

Let *r* cos *θ* = and *r* sin *θ* = 1

On squaring and adding, we obtain

This is the required polar form.

#### Question 8:

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

#### Answer:

*i*

Let *r* cos*θ* = 0 and *r* sin *θ* = 1

On squaring and adding, we obtain

This is the required polar form.