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Complex Numbers

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  1. 301.The sum of all the real values of x satisfying 2^(x-1)(x^2+5x-50)=1 is:
  2. 302.Let p(x) be a quadratic polynomial such that p(0)=1.
  3. 303.A value of for which 2+3i1-2i is purely imaginary, is:
  4. 304.The point represented by 2+i in the Argand plane moves 1 unit eastwards, then 2 units nort…
  5. 305.The sum of all real values of x satisfying (x^2-5x+5)^x^2+4x-60=1 is:
  6. 306.If x is a solution of √2x+1-√2x-1=1, x12, then 4x^2-1 is equal to:
  7. 307.If the equations x^2+bx-1=0 and x^2+x+b=0 have a common root different from -1, then |b| i…
  8. 308.If z is a non-real complex number, then the minimum value of Imz^5(Imz)^5 is:
  9. 309.A complex number z is said to be unimodular if |z|=1.
  10. 310.Let and be the roots of x^2-6x-2=0.
  11. 311.If the two roots of (a-1)(x^4+x^2+1)+(a+1)(x^2+x+1)^2=0 are real and distinct, then the se…
  12. 312.If 2+3i is one of the roots of 2x^3-9x^2+kx-13=0, k R, then the real root of this equation…
  13. 313.If z is a complex number such that |z|2, then the minimum value of |z+12|:
  14. 314.For all complex numbers z of the form 1+i, R, if z^2=x+iy, then
  15. 315.Let z-i be any complex number such that z-iz+i is a purely imaginary number.
  16. 316.If z_1,z_2 and z_3,z_4 are 2 pairs of complex conjugate numbers, then z_1z_4+z_2z_3 equals…
  17. 317.Let w (Imw0) be a complex number.
  18. 318.If a R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] denotes the greatest integer…
  19. 319.The equation √3x^2+x+5=x-3, where x is real, has:
  20. 320.The sum of the roots of x^2+|2x-3|-4=0, is:
  21. 321.If and are roots of x^2-4√2kx+2e^4 k-1=0 for some k, and ^2+^2=66, then ^3+^3 is equal to:
  22. 322.If 1 and 1 are the roots of ax^2+bx+1=0 (a0, a,b R), then x(x+b^3)+(a^3-3abx)=0 has roots:
  23. 323.If non-zero real numbers b and c are such that f(x)> g(x), where f(x)=x^2+2bx+2c^2 and g(x…
  24. 324.If equations ax^2+bx+c=0 (a,b,c R, a0) and 2x^2+3x+4=0 have a common root, then a:b:c equa…
  25. 325.If z is a complex number of unit modulus and argument , then (1+z1+ z) equals:
  26. 326.Let z satisfy |z|=1 and z=1-z.
  27. 327.Let a=Im(1+z^22iz), where z is any non-zero complex number.
  28. 328.If Z_10 and Z_2 be two complex numbers such that Z_2Z_1 is a purely imaginary number, then…
  29. 329.If p and q are non-zero real numbers, ^3+^3=-p, =q, then a quadratic equation whose roots …
  30. 330.If and are roots of x^2+px+3p4=0 such that |-|=√10, then p belongs to the set:
  31. 331.If a complex number z satisfies the equation z+√2|z+1|+i=0, then |z| is equal to:
  32. 332.If the equations x^2+2x+3=0 and ax^2+bx+c=0 (a,b,c R) have a common root, then a:b:c is
  33. 333.The least integral value of x such that x-5x^2+5x-14>0 satisfies:
  34. 334.The values of 'a' for which one root of x^2-(a+1)x+a^2+a-8=0 exceeds 2 and the other is le…
  35. 335.|z_1+z_2|^2+|z_1-z_2|^2 is equal to:
  36. 336.Let Z and W be complex numbers such that |Z|=|W|, and Z denotes the principal argument.
  37. 337.Let Z_1 and Z_2 be any two complex numbers.
  38. 338.If z1 and z^2z-1 is real, then the point represented by the complex number z lies:
  39. 339.Let p,q,r R and r>p>0.
  40. 340.If the sum of the squares of the roots of x^2-(-2)x-(1+)=0 is least, then is equal to
  41. 341.The value of k for which (k-2)x^2+8x+k+4=0 has both roots real, distinct and negative, is
  42. 342.If (1) is a cube root of unity, and (1+)^7=A+B, then (A,B) equals
  43. 343.Let a a_10, f(x)=ax^2+bx+c, g(x)=a_1x^2+b_1x+c_1, and p(x)=f(x)-g(x).
  44. 344.Sachin and Rahul attempted to solve a quadratic equation.
  45. 345.Let , be real and z be a complex number.
  46. 346.The number of complex numbers z such that |z-1|=|z+1|=|z-i| equals
  47. 347.If and are the roots of x^2-x+1=0, then ^2009+^2009=
  48. 348.If the roots of bx^2+cx+a=0 are imaginary, then for all real values of x, the expression 3…
  49. 349.If z-4z=2, then the maximum value of |z| is equal to:
  50. 350.The quadratic equations x^2-6x+a=0 and x^2-cx+6=0 have one root in common.