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

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

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 cosθ = 0 and r sin θ = 1

On squaring and adding, we obtain

This is the required polar form.