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.
Answer:
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