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

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Question 18:

Match the statements of column A and B.


Match the Statement Column A and B

Column A

Column B


The value of is


Purely imaginary complex number


The value of is


Purely real complex number


Conjugate of lies in


Second quadrant


lies in


Fourth quadrant


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


May not occur in conjugate pairs


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


May occur in conjugate pairs


(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



Therefore which do not form a conjugate pair.

Question 19:

What is the value of


i, because

Question 20:

What is the smallest positive integer , for which ?



which is possible if

Question 21:

What is the reciprocal of


Reciprocal of

Therefore, reciprocal of

Question 22:

If then find the quadrant in which lies.


Which is represented by a point in first quadrant.

Question 23:

What is the conjugate of ?



Therefore, the conjugate of

Question 24:

What is the principal value of amplitude of ?


Let be the principle value of amplitude of . Since

Question 25:

What is the polar form of the complex number ?


Polar form of