# NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 4

Get top class preparation for IMO right from your home: fully solved questions with step-by-step explanation- practice your way to success.

Question 8:

If are complex numbers such that

, then find the value of

Given that

Question 9:

If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre , find the greatest and least values of

Distance of the point representing from the centre of the circle is

According to given condition .

Now

Therefore, greatest value of is .

Since least value of the modulus of a complex number is zero, the least value of

Question 10:

Locate the points for which

which is the interior of circle with centre at origin and radius 4 units, and which is exterior of circle with centre at origin and radius 3 units. Hence is the portion between two circles and .

Question 11:

Find the value of when

Therefore

Question 12:

Find the value of P such that the difference of the roots of the equation is

Let be the roots of the equation

Therefore

Now

Therefore

Question 13:

Find the value of a such that the sum of the squares of the roots of the equation is least.

Let be the roots of the equation

Therefore, and

Now

Therefore, will be minimum if

Question 14:

Find the value of k if for the complex numbers