# NCERT Class 11-Math՚S: Chapter – 5 Complex Numbers and Quadratic Equations Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for IMO-Level-2 Class-5 right from your home: Get full length tests using official NTA interface: all topics with exact weightage, real exam experience, detailed analytics, comparison and rankings, & questions with full solutions, fully solved questions with step-by-step explanation- practice your way to success.

**Question 2**:

If where show that

**Answer**:

i.e.. ,

Thus

So, .

**Question 3**:

Solve the equation where

**Answer**:

From (2) , we have

When from (1) , we get i.e.. , .

When from (1) , we get

Hence, the solutions of the given equation are

**Question 4**:

If the imaginary part of is , then show that the locus of the point representing in the Argand plane is a straight line.

**Answer**:

Let Then

Thus

But

So

, which is the equation of a line.

**Question 5**:

If , then show that *z* lies on imaginary axis.

**Answer**:

Let Then

Hence z lies on

**Question 6**:

Let and be two complex numbers such that and Then find

**Answer**:

Given that

Thus

**Question 7**:

Let and be two complex numbers such that .

Then show that .

**Answer**:

Let and

Where .

We have,