questionrEarly access

Complex Numbers

Showing 50 of 455 · 455 total
  1. 351.The conjugate of a complex number is 1i-1.
  2. 352.If |z+4|3, then the maximum value of |z+1| is
  3. 353.If the difference between the roots of x^2+ax+1=0 is less than √5, then the set of possibl…
  4. 354.All the values of m for which both roots of x^2-2mx+m^2-1=0 are greater than -2 but less t…
  5. 355.If the roots of x^2+px+q=0 are 30^ and 15^ respectively, then the value of 2+q-p is
  6. 356.If z^2+z+1=0, where z is a complex number, then the value of (z+1z)^2+(z^2+1z^2)^2+(z^3+1z…
  7. 357.If x is real, the maximum value of 3x^2+9x+173x^2+9x+7 is
  8. 358.If = zz-13i and ||=1, then z lies on
  9. 359.If z_1 and z_2 are two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then z_1-…
  10. 360.If the cube roots of unity are 1,,^2, then the roots of (x-1)^3+8=0 are
  11. 361.In a triangle PQR, R=2.
  12. 362.If the roots of x^2-bx+c=0 are two consecutive integers, then b^2-4c equals
  13. 363.If both roots of x^2-2kx+k^2+k-5=0 are less than 5, then k lies in the interval
  14. 364.The value of a for which the sum of the squares of the roots of x^2-(a-2)x-a-1=0 assumes t…
  15. 365.If z=x-iy and z^1/3=p+iq, then ( xp+ yq)/(p^2+q^2) is equal to
  16. 366.Let z and w be complex numbers such that z+iw=0 and (zw)=.
  17. 367.If |z^2-1|=|z|^2+1, then z lies on
  18. 368.If one root of x^2+px+12=0 is 4, while x^2+px+q=0 has equal roots, then the value of q is
  19. 369.If (1-p) is a root of x^2+px+(1-p)=0, then its roots are
  20. 370.If (1+i1-i)^x=1, then
  21. 371.If z and are two non-zero complex numbers such that |z|=1 and Arg(z)-Arg()=2, then z is eq…
  22. 372.The number of real solutions of x^2-3|x|+2=0 is
  23. 373.The value of 'a' for which one root of (a^2-5a+3)x^2+(3a-1)x+2=0 is twice as large as the …
  24. 374.Let Z_1 and Z_2 be two roots of Z^2+aZ+b=0, Z complex.
  25. 375.If |z-4|<|z-2|, its solution is given by
  26. 376.z and w are two non-zero complex numbers such that |z|=|w| and Arg(z)+Arg(w)=.
  27. 377.The locus of the centre of a circle which touches the circle |z-z_1|=a and |z-z_2|=b exter…
  28. 378.If p and q are the roots of x^2+px+q=0, then
  29. 379.Product of real roots of the equation t^2x^2+|x|+9=0
  30. 380.Difference between the corresponding roots of x^2+ax+b=0 and x^2+bx+a=0 is the same, and a…
  31. 381.If but ^2=5-3 and ^2=5-3, then the equation having / and / as its roots is
  32. 382.All the points in the set S=+i-i: R (i=-1) lie on a:
  33. 383.z and w are two nonzero complex numbers such that [,| z | = | w |] and Arg z + Arg w =[ ] …
  34. 384.The locus of the centre of a circle which touches the circle [| z - z_1 | = a] and[| z - z…
  35. 385.Let Z_1 and Z_2 be two roots of the equation Z^2 + aZ + b = 0, Z being complex.
  36. 386.Let z and w be complex numbers such that [ z + i w = 0] and arg zw = [ ].
  37. 387.If the cube roots of unity are 1, [ ,,, ^2] then the roots of the equation (x - 1)^3 + 8 =…
  38. 388.If [, = z z - 1 3i,] and [| | = 1], then z lies on :
  39. 389.If z_1 and z_2 are two non-zero complex numbers such that [,| z_1 + z_2 | = | z_1 | + | z_…
  40. 390.If z^2 + z + 1 = 0, where z is complex number, then value of [( z + 1 z )^2 + ( z^2 + 1 z^…
  41. 391.If [,| z - 4 z | = 2,] then the maximum value of [,| z |] is equal to :
  42. 392.If z is a complex number of unit modulus and argument [ ], then arg [( 1 + z 1 + z )] equa…
  43. 393.If z is a complex number such that [,| z | 2,], then the minimum value of [,,| z + 1 2 |] …
  44. 394.A complex number z is said to be unimodular if [,| z | = 1].
  45. 395.The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units no…
  46. 396.Let z[ ]C, the set of complex numbers.
  47. 397.If [ , C] are the distinct roots of the equation x2 - x + 1 = 0, then [ ^101 + ^107] is eq…
  48. 398.The set of all [ ] [ ] R, for which w = [1 + ( 1 - 8 )z 1 - z] is purely imaginary number,…
  49. 399.If z and w are two complex numbers such that |zw| = 1 and arg(z) -- arg(w) = [ 2] , then :
  50. 400.Let [z = ( 3 2 + i 2 )^5 + ( 3 2 - i 2 )^5.] If R(z) and 1(z) respectively denote the real…