## 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 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.

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