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Complex Numbers One Mark Questions

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

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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 x 2 + y 2 = 1 then the value of (a) x – iy (b) 2x (c) – 2iy(d) x + iy

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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 = (a 1 + ib 1 ) (a 2 + ib 2 ) (a 3 + ib 3 ), then A 2 + B 2 is (a) a b a b a b 3 2 (b) (a 1 + a 2 + a 3 ) 2 + (b 1 + b 2 + b 3 ) 2 (c) (a b 1 2 )(a b 2 2 )(a b 3 2 ) (d) (a a a 3 2 )(b b b 3 2 )

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Choose the Correct Answer 7. The points z 1, z 2, z 3, z 4 in the complex plane are the vertices of a parallelogram in order if and only if (a) z 1 + z 4 = z 2 + z 3 (b) z 1 + z 3 = z 2 + z 4 (c) z 1 + z 2 = z 3 + z 3 (d) z 1 – z 2 = z 3 – z 4 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

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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

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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 (i 25 ) 3 is (a) cos /2 + isin /2 (b) cos + isin (c) cos – isin (d) cos /2 – isin /2

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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 x 2 + y 2 – 4x – 1 = The value of is (a) cos + isin (b) cos – isin (c) sin – icos (d) sin – icos

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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 z n = cos + isin then z 1 z 2 z 3 …..z 6 is (a) 1 (b) –1 (c) i (d) – i

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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 (a 2 c 2 – b 2 )/abc is (a) cos2( – + ) + isin2( – + ) (b) –2cos( – + ) (c) – 2isin( – + ) (d) 2cos( – + )

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Choose the Correct Answer 19. If z 1 = 4 + 5i, z 2 = – 3 + 2i then the value of is (a) (b) (c) (d) 20. The value of i + i 22 + i 23 + i 24 + i 25 is (a) i(b) –i (c) 1 (d) – 1

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Choose the Correct Answer 21. The conjugate of i 13 + i 14 + i 15 + i 16 is (a) 1 (b) – 1 (c) 0 (d) – i 22. If – i + 2 is one root of the equation ax 2 – bx + c = 0, then the other root is (a) – i – 2 (b) i – 2 (c) 2 + i (d) 2i + 1

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Choose the Correct Answer 23. The quadratic equation whose roots are i 7 is (a) x = 0(b) x 2 – 7 = 0 (c) x 2 + x + 7 = 0 (d) x 2 – x – 7 = The equation having 4 – 3i and 4 + 3i as roots is (a) x 2 + 8x + 25 = 0 (b) x 2 + 8x – 25 = 0 (c) x 2 – 8 x + 25 = 0 (d) x 2 – 8x – 25 = 0

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Choose the Correct Answer 25. If is a root of the equation ax 2 + 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 x 2 – 6x + k = 0 then k is (a) 5 (b) 5 (c) 10 (d) 10

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Choose the Correct Answer 27. If is a cube root of unity, then the value of (1 – + 2 ) 4 + (1 + – 2 ) 4 is (a) 0(b) 32 (c) – 16 (d) – If is a cube root of unity, then the value of (1 – )(1 – 2 )(1 – 4 )(1 – 8 ) is (a) 9 (b) – 9 (c) 16 (d) 32

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

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Choose the Correct Answer 31.The complex number form of is (a) (b) – (c) (d) 35i 32.The complex number form of 3 – is (a) (b) (c) 3 – i7 (d) 3 + i7

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Choose the Correct Answer 33.Real and imaginary parts of are (a) 4, 3 (b) 4, – 3 (c) – 3, 4 (d) 3, 4 34.The complex conjugate of is (a) (b) (c) (d) 35.Real and imaginary parts of 3/2 i are (a) 0, 3/2 (b) 3/2, 0 (c) 2, 3(d) 3, 2

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Choose the Correct Answer 36.The complex conjugate of – 4 – 9i (a) – 4 + 9i (b) 4 + 9i (c) 4 – 9i (d) – 4 – 9i 37.The complex conjugate of 5 is (a) 5 (b) – 5 (c) i 5 (d) – i 5 38.The standard form (a + ib) of 3 + 2i + (– 7 – i) is (a) 4 – i(b) – 4 + i (c) 4 + i(d) 4 + 4i

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Choose the Correct Answer 39.If a + ib = (8 – 6i) – (2i – 7) then the values of a and b are (a) 8, –15 (b) 8, 15 (c) 15, 9(d) 15, – 8 40.If p + iq = (2 – 3i)(4 + 2i) then q is (a) 14(b) – 14 (c) – 8 (d) 8 41.The conjugate of (2 + i)(3 – 2i) is (a) 8 – i(b) – 8 – i (c) – 8 + i (d) 8 + i

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Choose the Correct Answer 42.The real and imaginary parts of (2 + i)(3 – 2i) are (a) – 1, 8(b) – 8, 1 (c) 8, – 1 (d) – 8, – 1 43.The modulus values of – 2 + 2i and 2 – 3i are (a) 5, 5(b) 2 5, 13 (c) 2 2, 13(d) – 4, 1 44.The modulus values of – 3 – 2i and 4 + 3i are (a) 5, 5(b) 5, 7 (c) 6, 1(d) 13, 5

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Choose the Correct Answer 45.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 46.The arguments of nth roots of a complex number differ by (a) (b) (c) (d)

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Choose the Correct Answer 47.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 48.If | z – z 1 | = | z – z 2 | then the locus of z is (a) a circle with center at the origin (b) a circle with center at z 1 (c) a straight line passing through the origin (d) is a perpendicular bisector of the line joining z 1 and z 2

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Choose the Correct Answer 49.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 50.The value of is (a) 2Re(z) (b) Re(z) (c) Im(z)(d) 2Im(z)

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Choose the Correct Answer 51.The value of is (a) 2Im(z) (b) 2i Im(z) (c) Im(z)(d) i Im(z) 52.The value of is (a) | z |(b) | z | 2 (c) 2| z |(d) 2| z | 2 53.The fourth roots of unity are (a) 1 i, – 1 i (b) i, 1 i (c) 1, i (d) 1, – 1

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Choose the Correct Answer 54.If is a cube root of unity then (a) 2 = 1 (b) 1 + = 0 (c) 1 + + 2 = 0(d) 1 – + 2 = 0 55.The principal value of arg z lies in the interval (a) (b) (– , ] (c) [0, ](d) (– , 0] 56.The fourth roots of unity form the vertices of (a) an equilateral triangle(b) a square (c) a hexagon(d) a rectangle

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Choose the Correct Answer 57.If z 1 and z 2 are any two complex numbers then which one of the following is false (a) Re(z 1 + z 2 ) = Re(z 1 ) + Re(z 2 ) (b) Im(z 1 + z 2 ) = Im(z 1 ) + Im(z 2 ) (c) arg(z 1 + z 2 ) = arg(z 1 ) + arg(z 2 ) (d) | z 1 z 2 | = | z 1 | | z 2 | 58.Cube roots of unity are (a) 1, (b) i, (c) 1, (d) i,

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Choose the Correct Answer 59.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 60.The value of e i + e – i is (a) 2 cos (b) cos (c) 2sin (d) sin 61.The value of e i – e – i is (a) sin (b) 2sin (c) isin (d) 2i sin

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Choose the Correct Answer 62.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 63.If z 1 = a + ib, z 2 = - a + ib then z 1 – z 2 lies on (a) real axis(b) imaginary axis (c) the line y = x(d) the line y = – x

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Choose the Correct Answer 64. 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 65.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

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Choose the Correct Answer 66.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

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Choose the Correct Answer 67.Which of the following is not true? (a) (b) (c) Re(z) = (d) Im(z) = 68.If z 1 and z 2 are complex numbers then which of the following is meaningful? (a) z 1 z 2 (c) z 1 z 2 (d) z 1 z 2

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Choose the Correct Answer 69.Which of the following is incorrect? (a) Re (z) | z | (b) Im (z) | z | (c) z = | z | 2 (d) Re (z) | z | 70.Which of the following is incorrect? (a) | z 1 + z 2 | | z 1 | + | z 2 | (b) | z 1 – z 2 | | z 1 | + | z 2 | (c) | z 1 – z 2 | | z 1 | – | z 2 | (d) | z 1 + z 2 | | z 1 | + | z 2 |

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Choose the Correct Answer 71.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, – ) 72.Which of the following is an incorrect regarding n th 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

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Choose the Correct Answer 73.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

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