# CBSE Class 11 – Mathematics: Complex Numbers: Exercise – 1 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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: