# NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 3

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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,