NCERT Class 11-Math՚S: Chapter – 5 Complex Numbers and Quadratic Equations Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 8:

If are complex numbers such that

, then find the value of

Answer:

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

Answer:

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

Answer:

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

Answer:

Therefore

Question 12:

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

Answer:

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.

Answer:

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

Answer:

L. H. S.

R. H. S.

Hence, equating LHS and RHS, we get .