# NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 9

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**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:**