## NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations Ex 5.2

#### Question 1:

Find the modulus and the argument of the complex number

On squaring and adding, we obtain
Since both the values of sin θ and cos θ are negative and sinθ and cosθ 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

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

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

– 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

– 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

–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:

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