NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 6

Get top class preparation for ISAT Class-5 right from your home: Get full length tests using official NTA interface: all topics with exact weightage, real exam experience, detailed analytics, comparison and rankings, & questions with full solutions.

Question 18:

Match the statements of column A and B.

Answer:

Match the Statement Column A and B

Column A

Column B

(a)

The value of is

(i)

Purely imaginary complex number

(b)

The value of is

(ii)

Purely real complex number

(c)

Conjugate of lies in

(iii)

Second quadrant

(d)

lies in

(iv)

Fourth quadrant

(e)

If and then the roots of the equation are non-real (complex) and

(v)

May not occur in conjugate pairs

(f)

If a, b, and , and is a perfect square, then the roots of the equation

(vi)

May occur in conjugate pairs

Answer:

(a) (ii), because (which is purely a real complex number)

(b) (i), because which is purely imaginary complex number.

(c) (iv), conjugate of is , which is represented by the point in the fourth quadrant.

(d) (iii), because which is represented by the point in the second quadrant.

(e) (vi), If square root of D is imaginary number, therefore, roots are roots are in conjugate pairs.

(e) (v), Consider the equation where

clearly

Now

Therefore which do not form a conjugate pair.

Question 19:

What is the value of

Answer:

i, because

Question 20:

What is the smallest positive integer , for which ?

Solution:

because

which is possible if

Question 21:

What is the reciprocal of

Answer:

Reciprocal of

Therefore, reciprocal of

Question 22:

If then find the quadrant in which lies.

Answer:

Which is represented by a point in first quadrant.

Question 23:

What is the conjugate of ?

Answer:

Let

Therefore, the conjugate of

Question 24:

What is the principal value of amplitude of ?

Answer:

Let be the principle value of amplitude of . Since

Question 25:

What is the polar form of the complex number ?

Answer:

Polar form of