NCERT Class 11-Math՚S: Chapter – 5 Complex Numbers and Quadratic Equations Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 26:

What is the locus of z, if amplitude of is ?

Answer:

Let . Then

Let be the amplitude of . Then

Hence, the locus of is a straight line.

Question 27:

If , is a root of the equation , where , then find the values of and .

Answer:

Sum of roots

(Since non real complex roots occur in conjugate pairs)

Product of roots,

Choose the correct options out of given four options in each of the Examples from 28 to 33 (M. C. Q.) .

Question 28:

is

(A) Positive

(B) negative

(C) 0

(D) can-not be evaluated

Answer: (D)

which can not be evaluated unless n is known.

Question 29:

If the complex number satisfies the condition , then z lies on

Answer:

(A)

(B) Circle with centre and radius

(C) Circle with centre and radius

(D)

Answer: (C)

Which is a circle with centre and radius .

Question 30:

The area of the triangle on the complex plane formed by the complex numbers and is:

(A)

(B)

(C)

(D) None of these

Answer: (C)

Let Then . Therefore,

Required area of the triangle

Question 31:

The equation represents a

(A) Straight line

(B) Circle

(C) Parabola

(D) Hyperbola

Answer: (A)

, where A denotes the point , B denotes the point and denotes the point

lies on the perpendicular bisector of the line joining A and B and perpendicular bisector is a straight line.