# NCERT Class 11-Math՚s: Chapter – 5 Complex Numbers and Quadratic Equations Part 3 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**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,