# NCERT Class 11-Math՚S: Chapter – 5 Complex Numbers and Quadratic Equations Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for NSTSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.

**Question 8**:

If , then show that where , represents a circle.

**Answer**:

Given

Now,

This is the equation of a circle.

**Question 9**:

If the real part of is , then show that the locus of the point representing in the complex plane is a circle.

**Answer**:

Let

Now,

Given that real part is

Which represents a circle.

Hence, locus of z is a circle.

**Question 10**:

Show that the complex number *z*, satisfying the condition lies on a circle.

**Answer**:

Let

Given

Which represents a circle.

**Question 11**:

Solve the equation .

**Answer**:

## Long Answer Type

**Question 12**:

If , then find z.

**Answer**:

**Question 13**:

If , then find . Where

**Answer**:

**Question 14**:

Show that represents a circle. Find its centre and radius.

**Answer**:

**Question 15**:

If is a purely imaginary number , then find the value of .

**Answer**: