1. Complex Numbers One Mark Questions PREPARED BY:
R.RAJENDRAN. M.A., M. Sc., M. Ed.,
K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,
CHENNAI-21

2. Choose the Correct Answer
1. The value of (a) (b) 0 (c) – (d) 1
2. The modulus and amplitude of the complex number [e3 – i /4]3 are respectively (a) (b) (c) (d)

3. Choose the Correct Answer
3. If (m – 5) + i(n + 4) is the complex conjugate of (2m + 3) + i(3n – 2), then (n, m) are (a) (– ½, –8) (b) (– ½, 8) (c) (½, –8) (d) (½, 8)
4. If x2 + y2 = 1 then the value of (a) x – iy (b) 2x (c) – 2iy (d) x + iy

4. Choose the Correct Answer
5. The modulus of the complex number 2 + i3 is (a) 3 (b) 13 (c) 7 (d) 7
6. If A + iB = (a1 + ib1) (a2 + ib2) (a3 + ib3), then A2 + B2 is (a) a12 + b12 + a22 + b22 + a32 + b32 (b) (a1 + a2 + a3)2 + (b1 + b2 + b3)2 (c) (a12 + b12)(a22 + b22)(a32 + b32) (d) (a12 + a22 + a32)(b12 + b22 + b32)

5. Choose the Correct Answer
7. The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram in order if and only if (a) z1+ z4 = z2 + z3 (b) z1+ z3 = z2 + z4 (c) z1+ z2 = z3 + z3 (d) z1 – z2 = z3 – z4
8. If a = 3 + i and z = 2 – i, then the points on the Argand diagram representing az, 3az and – az are (a) vertices of a right angled triangle (b) vertices of an equilateral triangle (c) vertices of an isosceles triangle (d) collinear

6. Choose the Correct Answer
9. If z represents a complex number then arg (z) + arg ( ) is (a) /4 (b) /2 (c) 0 (d) /3
10. If the amplitude of a complex number is /2 then the number is (a) purely imaginary (b) purely real (c) 0 (d) neither real nor imaginary

7. Choose the Correct Answer
11. If the point represented by the complex number iz is rotated about the origin through the angle /2 in the counter clockwise direction then the complex number representing the new position is (a) iz (b) – iz (c) –z (d) z
12. The polar form of the complex number (i25)3 is (a) cos /2 + isin /2 (b) cos  + isin  (c) cos  – isin  (d) cos /2 – isin /2

8. Choose the Correct Answer
13. If P represents the variable complex number z and if |2z – 1| = 2|z| then the locus of P is (a) the straight line x = ¼ (b) the straight line y = ¼ (c) the straight line z = ½ (d) the circle x2 + y2 – 4x – 1 = 0
14. The value of is (a) cos  + isin  (b) cos  – isin  (c) sin  – icos  (d) sin  – icos 

9. Choose the Correct Answer
15. If – lies in the third quadrant then z lies in the (a) First quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant
16. If zn = cos isin then z1z2z3…..z6 is (a) (b) –1 (c) i (d) – i

10. Choose the Correct Answer
17. If x = cos + isin, then the value of is (a) 2cos n (b) 2isin n (c) 2sin n (d) 2i cos n
18. If a = cos – isin, b = cos – isin , c = cos – isin then (a2c2 – b2)/abc is (a) cos2( –  + ) + isin2( –  + ) (b) –2cos( –  + ) (c) – 2isin( –  + ) (d) 2cos( –  + )

11. Choose the Correct Answer
19. If z1 = 4 + 5i, z2 = – 3 + 2i then the value of is (a) (b) (c) (d)
20. The value of i + i22 + i23 + i24 + i25 is (a) i (b) –i (c) (d) – 1

12. Choose the Correct Answer
21. The conjugate of i13 + i14 + i15 + i16 is (a) (b) – 1 (c) (d) – i
22. If – i + 2 is one root of the equation ax2 – bx + c = 0, then the other root is (a) – i – (b) i – 2 (c) 2 + i (d) 2i + 1

13. Choose the Correct Answer
23. The quadratic equation whose roots are i7 is (a) x2 + 7 = 0 (b) x2 – 7 = 0 (c) x2 + x + 7 = 0 (d) x2 – x – 7 = 0
24. The equation having 4 – 3i and 4 + 3i as roots is (a) x2 + 8x + 25 = 0 (b) x2 + 8x – 25 = 0 (c) x2 – 8 x + 25 = 0 (d) x2 – 8x – 25 = 0

14. Choose the Correct Answer
25. If is a root of the equation ax2 + bx + 1 = 0 where a, b are real then (a, b) is (a) (1, 1) (b) (1, –1) (c) (0, 1) (d) (1, 0)
26. If –i + 3 is a root of x2 – 6x + k = 0 then k is (a) (b) 5 (c)  (d) 10

15. Choose the Correct Answer
27. If  is a cube root of unity, then the value of (1 –  + 2)4 + (1 +  – 2)4 is (a) (b) 32 (c) – (d) – 32
28. If  is a cube root of unity, then the value of (1 – )(1 – 2)(1 – 4)(1 – 8) is (a) (b) – 9 (c) (d) 32

16. Choose the Correct Answer
29. Which one of the following is incorrect? (a) |z1z2| = |z1| |z2| (b) |z1 + z2|  |z1| + |z2| (c) |z1 – z2| > |z1| – |z2| (d) |z1 + z2|2 =(z1 + z2)( )
30. If  is nth root of unity, then (a) 1 + 2 + 4 + …… =  + 3 + 5+ ……. (b) n = 0 (c) n = (d)  = n – 1

17. Choose the Correct Answer
The complex number form of is (a) (b) – (c) (d) 35i
The complex number form of 3 – is (a) (b) (c) 3 – i7 (d) 3 + i7

18. Choose the Correct Answer
Real and imaginary parts of are (a) 4, 3 (b) 4, – 3 (c) – 3, (d) 3, 4
The complex conjugate of is (a) (b) (c) (d)
Real and imaginary parts of 3/2 i are (a) 0, 3/2 (b) 3/2, 0 (c) 2, (d) 3, 2

19. Choose the Correct Answer
The complex conjugate of – 4 – 9i (a) – 4 + 9i (b) 4 + 9i (c) 4 – 9i (d) – 4 – 9i
The complex conjugate of 5 is (a) 5 (b) –5 (c) i5 (d) – i5
The standard form (a + ib) of 3 + 2i + (– 7 – i) is (a) 4 – i (b) – 4 + i (c) 4 + i (d) 4 + 4i

20. Choose the Correct Answer
If a + ib = (8 – 6i) – (2i – 7) then the values of a and b are (a) 8, – (b) 8, (c) 15, (d) 15, – 8
If p + iq = (2 – 3i)(4 + 2i) then q is (a) (b) – (c) – (d) 8
The conjugate of (2 + i)(3 – 2i) is (a) 8 – i (b) – 8 – i (c) – 8 + i (d) 8 + i

21. Choose the Correct Answer
The real and imaginary parts of (2 + i)(3 – 2i) are (a) – 1, 8 (b) – 8, 1 (c) 8, – (d) – 8, – 1
The modulus values of – 2 + 2i and 2 – 3i are (a) 5, (b) 25, 13 (c) 22, 13 (d) – 4, 1
The modulus values of – 3 – 2i and 4 + 3i are (a) 5, (b) 5, 7 (c) 6, (d) 13, 5

22. Choose the Correct Answer
The cube roots of unity are (a) in GP with common ratio  (b) in GP with common difference 2 (c) in AP with common difference  (d) in AP with common difference 2
The arguments of nth roots of a complex number differ by (a) (b) (c) (d)

23. Choose the Correct Answer
Which of the following statements is correct? (a) negative complex numbers exist (b) order relation does not exist in real numbers (c) order relation exist in complex numbers (d) (1 + i) > (3 – 2i) is meaningless
If | z – z1 | = | z – z2 | then the locus of z is (a) a circle with center at the origin (b) a circle with center at z1 (c) a straight line passing through the origin (d) is a perpendicular bisector of the line joining z1 and z2

24. Choose the Correct Answer
Which of the following statement are correct? (1) Re (z)   z  (2) Im (z)   z  (3)   =  z  (4) | | =( )n (a) 1 and 2 (b) 2 and 3 (c) 2, 3 and 4 (d) 1, 3 and 4
The value of is (a) 2Re(z) (b) Re(z) (c) Im(z) (d) 2Im(z)

25. Choose the Correct Answer
The value of is (a) 2Im(z) (b) 2i Im(z) (c) Im(z) (d) i Im(z)
The value of is (a) | z | (b) | z |2 (c) 2| z | (d) 2| z |2
The fourth roots of unity are (a) 1  i, – 1  i (b)  i, 1  i (c)  1,  i (d) 1, – 1

26. Choose the Correct Answer
If  is a cube root of unity then (a) 2 = (b) 1 +  = 0 (c) 1 +  + 2 = 0 (d) 1 –  + 2 = 0
The principal value of arg z lies in the interval (a) (b) (–, ] (c) [0, ] (d) (–, 0]
The fourth roots of unity form the vertices of (a) an equilateral triangle (b) a square (c) a hexagon (d) a rectangle

27. Choose the Correct Answer
If z1 and z2 are any two complex numbers then which one of the following is false (a) Re(z1 + z2) = Re(z1) + Re(z2) (b) Im(z1 + z2) = Im(z1) + Im(z2) (c) arg(z1 + z2) = arg(z1) + arg(z2) (d) | z1 z2 | = | z1 | | z2 |
Cube roots of unity are (a) 1, (b) i, (c) 1, (d) i,

28. Choose the Correct Answer
The number of values of (cos  + isin)p/q where p and q are non-zero integers prime to each other, is (a) p (b) q (c) p + q (d) p – q
The value of ei + e – i is (a) 2 cos (b) cos (c) 2sin (d) sin
The value of ei – e – i is (a) sin (b) 2sin (c) isin (d) 2i sin

29. Choose the Correct Answer
Geometrical interpretation of is (a) reflection of z on real axis (b) reflection of z on imaginary axis (c) rotation of z about origin (d) rotation of z about origin through /2 in clockwise direction
If z1 = a + ib, z2 = - a + ib then z1 – z2 lies on (a) real axis (b) imaginary axis (c) the line y = x (d) the line y = – x

30. Choose the Correct Answer
Which one of the following is incorrect? (a) (cos  + isin )n = cos n + isin n (b) (cos  – isin )n = cos n – isin n (c) (sin  + icos )n = sin n + icos n (d) = cos  – isin 
Polynomial equation P(x) = 0 admits conjugate pairs of roots only if the coefficients are (a) imaginary (b) complex (c) real (d) either real or complex

31. Choose the Correct Answer
Identify the correct statement (a) sum of the moduli of two complex numbers is equal to their modulus of the sum (b) modulus of the product of the complex numbers is equal to sum of their moduli (c) arguments of the product of two complex numbers is the product of their arguments (d) arguments of the product of two complex numbers is equal to sum of their arguments

32. Choose the Correct Answer
Which of the following is not true? (a) (b) (c) Re(z) = (d) Im(z) =
If z1 and z2 are complex numbers then which of the following is meaningful? (a) z1 < z2 (b) z1 > z2 (c) z1  z2 (d) z1  z2

33. Choose the Correct Answer
Which of the following is incorrect? (a) Re (z)  | z | (b) Im (z)  | z | (c) z = | z |2 (d) Re (z)  | z |
Which of the following is incorrect? (a) | z1 + z2 |  | z1 | + | z2| (b) | z1 – z2 |  | z1 | + | z2| (c) | z1 – z2 |  | z1| – | z2| (d) | z1 + z2 |  | z1 | + | z2|

34. Choose the Correct Answer
Which of the following is incorrect? (a) is the mirror image of z on the real axis (b) the polar form of is (r, – ) (c) – z is the point symmetrical to z about the origin (d) the polar form of – z is(–r, – )
Which of the following is an incorrect regarding nth root of unity? (a) the number of distinct roots is n (b) the roots are in GP with common ratio cis (c) the arguments are in AP with common difference (d) product of the roots is 0 and the sum of the roots is 1

35. Choose the Correct Answer
Which of the following is incorrect? (a) multiplying a complex number by i is equivalent to rotating the number counter clockwise about the origin through an angle 90 (b) multiplying a complex number by – i is equivalent to rotating the number clockwise about the origin through an angle 90 (c) dividing a complex number by i is equivalent to rotating the number counter clockwise about the origin through an angle 90 (d)dividing a complex number by i is equivalent to rotating the number clockwise about the origin through an angle 90

36. THE END