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

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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,