# CBSE Class 11 – Mathematics: Complex Numbers: Exercise – 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 1**:

Express the given complex number in the form

**Question 2**:

Express the given complex number in the form

**Question 3**:

Express the given complex number in the form

**Question 4**:

Express the given complex number in the form

**Question 5**:

Express the given complex number in the form

**Question 6**:

Express the given complex number in the form :

**Question 7**:

Express the given complex number in the form

**Question 8**

Express the given complex number in the form

**Question 9**:

Express the given complex number in the form

**Question 10**

Express the given complex number in the form

**Question 11**:

Find the multiplicative inverse of the complex number .

**Question 12**:

Find the multiplicative inverse of the complex number

**Question 13**

Find the multiplicative inverse of the complex number

**Question 14**

Express the following expression in the form of .

**Solution 1**

Multiplying

Now we know that

So

**Solution 2**:

Now so and

**Solution 3**:

**Solution 4**:

Now

So

**Solution 5**:

**Solution 6**:

**Solution 7**:

Opening the bracket

**Solution 8**:

**Can be written as**

**Solution 9**:

**Solution 10**:

**Solution 11**:

Let

Conjugate is given by

Modulus is given by

Multiple inverse of any complex number z is given by

**Solution 12**:

Let

Conjugate is given by

Modulus is given by

Multiple inverse of any complex number is given by

**Solution 13**:

Let

Conjugate is given by

Modulus is given by

Multiple inverse of any complex number z is given by

**Solution 14**: