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Complex Numbers

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  1. 51.Let C be the circle in the complex plane with centre z_0=(1)/(2)(1+3i) and radius r=1.
  2. 52.For a C, let A=z C:Re(a+z)>Im(a+z) and B=z C:Re(a+z)(S1): If Re(a),Im(a)>0, then the set A…
  3. 53.Let w_1 be the point obtained by the rotation of z_1=5+4 i about the origin through a righ…
  4. 54.Let S=z=x+iy:(2z-3i)/(4z+2i), is, a, real, number.
  5. 55.Let the complex number z=x+iy be such that (2z-3i)/(2z+i) is purely imaginary.
  6. 56.Let A= (0,2 ):(1+2i )/(1-i ) is purely imaginary .
  7. 57.If for z= +i ,|z+2|=z+4(1+i), then + and are the roots of the equation :
  8. 58.Let a b be two non-zero real numbers.
  9. 59.The complex number z=i-1 ( )/(3)+i ( )/(3) is equal to :
  10. 60.Let z=(1+i)(1+2i)(1+3i) .(1+ni), where i=-1.
  11. 61.Let =-1+i√32 and =-1-i√32,i=-1.
  12. 62.If is a root of the equation x^2+x+1=0 and _k=1^n( ^k+1 ^k)^2=20, then n is equal to _____…
  13. 63.Let A=z C:|z-2-i|=3,B=z C:Re(z-iz)=2 and S=A B.
  14. 64.Let integers a,b [-3,3] be such that a+b 0.
  15. 65.Let , be the roots of the equation x^2-ax-b=0 with Im( )<Im( ).
  16. 66.The sum of the square of the modulus of the elements in the set z=a+ib:a,b Z,z C,|z-1| 1,|…
  17. 67.Let P=z C:|z+2-3i| 1 and Q=z C:z(1+i)+z(1-i) -8.
  18. 68.If denotes the number of solutions of |1-i|^x=2^x and =((|z|)/(arg(z))), where z=( )/(4)(1…
  19. 69.Let , be the roots of the equation x^2-√6x+3=0 such that Im( )>Im( ).
  20. 70.Let , be the roots of the equation x^2-x+2=0 with Im( )>Im( ).
  21. 71.Let the complex numbers and 1 lie on the circles |z-z_0|^2=4 and |z-z_0|^2=16 respectively…
  22. 72.If satisfies the equation x^2+x+1=0 and (1+ )^7=A+B +C ^2,A,B,C 0, then 5(3A-2B-C) is equa…
  23. 73.Let w=zz+k_1z+k_2iz+ (1+i),k_1,k_2 R.
  24. 74.Let S=z C-i,2i:z^2+8iz-15z^2-3iz-2 R.
  25. 75.For , ,z C and >1, if -1 is the radius of the circle |z- |^2+|z- |^2=2 , then | - | is equ…
  26. 76.If x^2+x+1=0, then the value of [(x+1x)^4+(x^2+1x^2)^4+(x^3+1x^3)^4++(x^25+1x^25)^4] is:
  27. 77.Let S=zC: 4z^2+ z=0.
  28. 78.Let S=zC: 3|2z-3(1+i)|7.
  29. 79.If z=√32+i2, then (z^201-i)^8 is equal to
  30. 80.Let S=zC: |z-6iz-2i|=1, |z-8+2iz+2i|=35.
  31. 81.Let z be a complex number such that |z-6|=5 and |z+2-6i|=5.
  32. 82.Let z be a complex number such that |z+2|=|z-2| and (z+3z-i)=4.
  33. 83.Let z_1,z_2,z_3 be three complex numbers on the circle |z|=1 with (z_1)=-4, (z_2)=0, (z_3)…
  34. 84.Let the curve z(1+i)+ z(1-i)=4, zC, divide the region |z-3|1 into two parts of areas and .
  35. 85.Let | z-i2 z+i|=13, zC, define a circle C with centre (0,).
  36. 86.Let O be the origin, the point A be z_1=√3+2√2 i, and the point B(z_2) be such that |z_2||…
  37. 87.Let z be a complex number such that |z|=1.
  38. 88.Let zC be such that z^2+3iz-2+i=2+3i.
  39. 89.If z_1,z_2,z_3C are the vertices of an equilateral triangle whose centroid is z_0, then _k…
  40. 90.Let _1=(8+i)+(7+4i) and _2=(1+8i)+(4+7i).
  41. 91.Among the statements: (S1): The set zC--i: |z|=1, z-iz+i is purely real contains exactly t…
  42. 92.If the locus of zC such that Re(z-12z+i)+Re( z-12 z-i)=2 is a circle of radius r and centr…
  43. 93.Let A=[0,2]: 1+10Re(2+i-3i)=0.
  44. 94.Let the complex numbers and 1/ lie on two circles determined by z_0=1+i.
  45. 95.Let , be the roots of the equation x^2-√6x+3=0 such that Im()>Im().
  46. 96.Answer: 46
  47. 97.If z is a complex number, then the number of common roots of the equations z^1985+z^100+1=…
  48. 98.If denotes the number of solutions of |1-i|^x=2^x (x R) and is [a value defined by a furth…
  49. 99.Let z_1 and z_2 be two complex numbers such that [a governing condition not preserved in t…
  50. 100.Let , N be roots of the equation x^2-70x+=0, where /2,/3 N.