NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 9

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Question 8:

If , then show that where , represents a circle.

Answer:

Given

Now,

This is the equation of a circle.

Question 9:

If the real part of is , then show that the locus of the point representing in the complex plane is a circle.

Answer:

Let

Now,

Given that real part is

Which represents a circle.

Hence, locus of z is a circle.

Question 10:

Show that the complex number z, satisfying the condition lies on a circle.

Answer:

Let

Given

Which represents a circle.

Question 11:

Solve the equation .

Answer:

Long Answer Type

Question 12:

If , then find z.

Answer:

Question 13:

If , then find . Where

Answer:

Question 14:

Show that represents a circle. Find its centre and radius.

Answer:

Question 15:

If is a purely imaginary number , then find the value of .

Answer: