NCERT Class 11 Chapter 5 Maths Complex Numbers and Quadratic Equation MCQ

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1. If (1-i / 1+i)100 = a + ib then

A. a = 2, b = – 1

B. a = 1, b = 0

C. a = 0, b = 1

D. a = – 1, b = 2

2. The equation | z + 1 – i| = | z – 1 + i| represents a

A. straight line

B. circle

C. parabola

D. hyperbola

3. The modulus of √2i - - √2i is:

A. 2

B. √2

C. 0

D. 2√2

4. Number of solutions of the equation z2 + |z|2 = 0 is

A. 1

B. 2

C. 3

D. infinitely many

5. 1 + i2 + i4 + i6 + ... + i2n is

A. positive

B. negative

C. 0

D. cannot be determined

6. If f (z) = z⁴ + 9^z3 + 35^z2 – z + 4, then the value of f (– 5 + 2 - √4 ) is:

A. – 160

B. 160

C. 610

D. 106

7. If z = 2 – 3i, then the value of z² – 4z + 13 is

A. 1

B. –1

C. 0

D. None of these

8. If x = 1 + i, then the value of the expression x⁴ –4x³ + 7x² – 6x + 3 is :

A. – 1

B. 1

C. 2

D. none of these

9. If c + i/c-i = a + ib, where a, b, c are real, then a² + b² is equal to:

A. 7

B. 1

C. c²

D. – c²

10. The least value of a such that the sum of the squares of the roots of the equation x² – (a – 2)x – (a + 1) = 0 is

A. a = – 1

B. a = 1

C. a = 0

D. a = 2

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11. If a ¹ b but a² = 5a – 3 and b² = 5b – 3 then the equation having a/b and b/a as its roots is

A. 3x² – 19x + 3 = 0

B. 3x² + 19x – 3 = 0

C. 3x² – 19x – 3 = 0

D. x² – 5x + 3 = 0

12. If x + iy = /3cos i sin 2 q + q + then 4x – x² – y² reduces to :

A. 2

B. 3

C. 4

D. 5

13. If (x + iy) (2 – 3i) = 4 + i, then

A. x = – 14/13, y = 5/13

B. x = 5/13, y = 14/13

C. x = 14/13, y = 5/13

D. x = 5/13, y = – 14/13

14. If | z – 4 | < | z – 2 |, its solution is given by

A. Re(z) > 0

B. Re(z) < 0

C. Re(z) > 3

D. Re(z) > 2

15. If | z + 4 | £ 3, then the maximum value of
| z + 1 | is

A. 6

B. 0

C. 4

D. 10

16. The conjugate of a complex number is 1 /i –1 then that complex number is

A. –1/i –1

B. 1 /i +1

C. –1/i +1

D. 1/i –1

17. If the conjugate of (x + iy) (1 – 2i) is 1 + i, then:

A. y = 3/5

B. x - iy = 1 - i /1 + 2i

C. x + iy = 1 - i /1 - 2i

D. x = 1/5

18. arg z + arg z; z ¹ 0 is equal to :

A. π/4

B. π

C. 0

D. π/2

19. For z = 3 - i , the principal value of arg (z) is

A. –p/6

B. –p/3

C. –p/2

D. –p/4

20. If z1 = √3 + i √3 and z2 = √3 + i , then in which quadrant (z1/z2) lies?

A. I

B. II

C. III

D. IV

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21. If z1 and z2 are two non-zero complex numbers such that | z1 + z2 | = | z1 | + | z2 | , then arg z1 – arg z2 is equal to

A. π/2

B. – π

C. 0

D. -π/2

22. If z = x + iy satisfies amp (z – 1) = amp (z + 3i) then the value of (x – 1) : y is equal to

A. 2 : 1

B. 1 : 3

C. – 1 : 3

D. none of these

23. If (1+i / 1-i)x - 1 then

A. x = 2n +1 , where n is any positive integer

B. x = 4n , where n is any positive integer

C. x = 2n , where n is any positive integer

D. x = 4n +1 , where n is any positive integer

24. If a + ib> c + id, then :

A. a > c, b > d

B. a > c, b ³ d

C. a > c, b = d = 0

D. none of these

25. The system of equations | z + 1 – i | = 2 and | z | = 3 has

A. no solution

B. one solution

C. two solutions

D. none of these