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Complex Numbers

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  1. 251.Let z=x+iy be a non-zero complex number such that z^2=i|z|^2, where i=-1.
  2. 252.If a and b are real numbers such that (2+)^4=a+b, where =-1+i√32, then a+b is equal to:
  3. 253.The imaginary part of (3+2-54)^1/2-(3-2-54)^1/2 can be:
  4. 254.If and are two roots of x^2-64x+256=0, then the value of ^3/8^5/8+^3/8^5/8 is:
  5. 255.If and are the roots of 2x(2x+1)=1, then is equal to:
  6. 256.The product of the roots of the equation 9x^2-18|x|+5=0 is:
  7. 257.If and are the roots of 7x^2-3x-2=0, then the value of 1-^2+1-^2 is equal to:
  8. 258.Let u=2z+iz-ki, z=x+iy and k>0.
  9. 259.Let 0 be in R.
  10. 260.If and are roots of x^2+px+2=0 and 1,1 are roots of 2x^2+2qx+1=0, then (-1)(-1)(+1)(+1) is…
  11. 261.The set of all real values of for which (^2+1)x^2-4 x+2=0 always has exactly one root in t…
  12. 262.Let and be the roots of 5x^2+6x-2=0.
  13. 263.If be the ratio of the roots of 3m^2x^2+m(m-4)x+2=0, and +1=1, then the least value of m i…
  14. 264.If one real root of 81x^2+kx+256=0 is the cube of the other root, a value of k is:
  15. 265.Consider the quadratic equation (c-5)x^2-2cx+(c-4)=0, c5.
  16. 266.The value of such that the sum of the squares of the roots of x^2+(3-)x+2= assumes the lea…
  17. 267.Let and be two roots of x^2+2x+2=0.
  18. 268.The number of all possible positive integral values of for which the roots of 6x^2-11x+=0 …
  19. 269.If both roots of x^2-mx+4=0 are real, distinct, and lie in [1,5], then m lies in the inter…
  20. 270.Let z_0 be a root of x^2+x+1=0.
  21. 271.If 5, 5r, 5r^2 are the lengths of the sides of a triangle, then r cannot be equal to:
  22. 272.If z-z+ ( R) is a purely imaginary number and |z|=2, then a value of is:
  23. 273.Let z_1 and z_2 be two complex numbers satisfying |z_1|=9 and |z_2-3-4i|=4.
  24. 274.Let z be a complex number such that |z|+z=3+i (where i=-1).
  25. 275.Let z_1 and z_2 be any two non-zero complex numbers such that 3|z_1|=4|z_2|.
  26. 276.Let A=(-2,):3+2i1-2i is purely imaginary.
  27. 277.Let (-2-13 i)^3=x+iy27 (i=-1), where x,y are real numbers.
  28. 278.If z=(√32+ i2)^5+(√32- i2)^5, and R(z),I(z) denote the real and imaginary parts, then:
  29. 279.Let z C with Im(z)=10, satisfying 2z-n2z+n=2i-1 for some natural number n.
  30. 280.The equation |Z-i|=|Z-1|, i=-1, represents:
  31. 281.If a>0 and Z=(1+i)^2a-i has magnitude 2√5, then -z is equal to:
  32. 282.If z and are two complex numbers such that |z|=1 and (z)-()=2, then z is equal to:
  33. 283.Let z C be such that |z|<1.
  34. 284.If z=√32+ i2 (i=-1), then (1+iz+z^5+iz^8)^9 is equal to:
  35. 285.If and are the roots of x^2+x-2=0, [0,2], then ^12+^12(^-12+^-12)(-)^24 is equal to:
  36. 286.The number of real roots of 5+|2^x-1|=2^x(2^x-2) is:
  37. 287.Let p,q R.
  38. 288.If m is chosen in the quadratic equation (m^2+1)x^2-3x+(m^2+1)=0 such that the sum of its …
  39. 289.The sum of the solutions of | x-2|+ x( x-4)+2=0, (x>0), is equal to:
  40. 290.If and are the roots of x^2-2x+2=0, then the least value of n for which ()^n=1 is:
  41. 291.The set of all R, for which w=1+(1-8)z1-z is a purely imaginary number, for all z C satisf…
  42. 292.The least positive integer n for which (1+i√31-i√3)^n=1, is
  43. 293.Let p,q,r be real numbers (p q, r0), such that the roots of 1x+p+1x+q=1r are equal in magn…
  44. 294.If an angle A of a ABC satisfies 5 A+3=0, then the roots of 9x^2+27x+20=0 are:
  45. 295.If A and B are the roots of 3x^2-10x-25=0, then the value of 3^2(A+B)-10(A+B)(A+B)-25^2(A+…
  46. 296.If f(x) is a quadratic expression such that f(1)+f(2)=0 and -1 is a root of f(x)=0, then t…
  47. 297.If , C are the distinct roots of x^2-x+1=0, then ^101+^107 is equal to:
  48. 298.If R is such that the sum of the cubes of the roots of x^2+(2-)x+(10-)=0 is minimum, then …
  49. 299.If |z-3+2i|4, then the difference between the greatest and least value of |z| is
  50. 300.If, for a positive integer n, the quadratic equation x(x+1)+(x+1)(x+2)++(x+n-1)(x+n)=10n h…