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,