Page 41 - Mathematics Class - XI

Case-Study Based Questions
Case-Study Based Questions

Two complex numbers z = a + ib and z = c + id are said to be equal if a = c and b = d.
1 2
Then, on the basis of above information. Answer the following questions.

1. If (4a – 6 ) + 2ib = –8b + (2 + a) i, then the real values of a and b are

1 7
(a) − , (b) 1 ,− 7 (c) 1 1 (d) None of these
,
4 8 4 8 4 8
2. If (2a + 3b) + i (b + a) = 4i, then the real values of a and b are
(a) –8, 8 (b) –12, 8 (c) 12, –8 (d) 12, –12

3. If x + iy = 1 i , then the value of x + y is
2
2
1 i
(a) 0 (b) –1 (c) 10 (d) 1
4. If (x + y) + i (x – y) = 4 + 6i, then xy is equal to

(a) 5 (b) –5 (c) 4 (d) –4

Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 2: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Q. 1. Assertion (A) : Consider Z and Z are two complex numbers such that |Z | = |Z | + |Z – Z |, then
1 2 1 2 1 2
Z
I m 1 0
Z 2
Reason (R) : arg (z) = 0, it indicate that Z is purely real.

Q. 2. Assertion (A) : If P and Q are the points in the plane XOY representing the complex numbers Z and
1
Z respectively, then distance |PQ| = |Z – Z |
2 2 1
Reason (R) : Locus of the point P (z) satisfying |Z – (2 + 3i)| = 4 is a straight line.

Answers

Case-Study Based Questions: 1. (a) 2. (c) 3. (d) 4. (b)

Assertion-Reason Based Questions: 1. (a) 2. (c)

39