(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