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Complex Numbers

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  1. 401.Let z1 and z2 be any two non-zero complex numbers such that [3| z_1 | = 4| z_2 |.] If [z =…
  2. 402.Let [( - 2 - 1 3i )^3 = x + iy 27( i = - 1 ),,,] where x and y are real numbers, then y - …
  3. 403.Let z [ ] C with Im(z) = 10 and it satisfies [2z - n 2z + n] = 2i - 1 for some natural num…
  4. 404.Let z1 and z2 be two complex numbers satisfying, z1, = 9 and, z2 -- 3 -- 4i, = 4.
  5. 405.If [z = 3 2 + i 2( i = - 1 )], then (1 + iz + z5 + iz8)9 is equal to :
  6. 406.If [ ] and [ ] be the roots of the equation x2 -- 2x + 2 = 0, then the least value of n fo…
  7. 407.Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz_0^81 - 3iz_0^93…
  8. 408.Let [ ] and [ ] be two roots of the equation x2 + 2x + 2 = 0 , then [ ^15] + [ ^15] is equ…
  9. 409.If z1 , z2 are complex numbers such that Re(z1) = |z1 -- 1|, Re(z2) = |z2 -- 1| , and arg(…
  10. 410.If the four complex numbers [z, z , z - 2 Re ( z )] and z-2Re(z) represent the vertices of…
  11. 411.The region represented by z = x + iy [ ] C : |z| -- Re(z) [ ] 1 is also given by the inequ…
  12. 412.If z be a complex number satisfying Re(z)| + |Im(z)| = 4, then |z| cannot be :
  13. 413.Let z be complex number such that [| z - i z + 2i | = 1] and |z| = [5 2].
  14. 414.The least value of |z| where z is complex number which satisfies the inequality [ ( (|z| +…
  15. 415.Let a complex number z, |z| [] 1, satisfy [ _1 2 ( |z| + 11 (|z| - 1)^2 ) 2].
  16. 416.Let S1, S2 and S3 be three sets defined as S1 = z[]C : |z - 1| [ ] [ 2 ] S2 = z[]C : Re((1…
  17. 417.The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :
  18. 418.Let a complex number be w = 1 - [ 3 ]i.
  19. 419.If the equation [a|z|^2 + z + z + d = 0] represents a circle where a, d are real constants…
  20. 420.If z and [] are two complex numbers such that [| z | = 1] and [ (z) - ( ) = 3 2], then [ (…
  21. 421.Let n denote the number of solutions of the equation z2 + 3[ z ] = 0, where z is a complex…
  22. 422.If [], [] [] R are such that 1 - 2i (here i2 = -1) is a root of z2 + []z + [] = 0, then ([…
  23. 423.Let C be the set of all complex numbers.
  24. 424.For [n N], let [S_n=z C:|z-3+2 i|=n4] and [T_n=z C:|z-2+3 i|=1n].
  25. 425.Let z1 and z2 be two complex numbers such that [ z _1 = i z _2] and [ ( z_1 z _2 ) = ].
  26. 426.If z=x+i y satisfies |z|-2=0 and |z-i|-|z+5 i|=0, then :
  27. 427.Let O be the origin and A be the point z_1 = 1 + 2i.
  28. 428.Let the minimum value v_0 of [v=|z|^2+|z-3|^2+|z-6 i|^2, z C] is attained at z=z_0.
  29. 429.Let [S_1=z_1 C:|z_1-3|=(1)/(2)] and [S_2=z_2 C:|z_2-| z_2+1||=|z_2+| z_2-1||].
  30. 430.If [z 0] be a complex number such that [|z-(1)/(z)|=2], then the maximum value of |z| is :
  31. 431.If z=2+3 i, then [z^5+(z)^5] is equal to :
  32. 432.Let arg(z) represent the principal argument of the complex number z.
  33. 433.Let [] and [] be the roots of the equation x2 + (2i - 1) = 0.
  34. 434.The real part of the complex number [(1 + 2i)^8,.,(1 - 2i)^2 (3 + 2i),., (4 - 6i) ] is equ…
  35. 435.For [a C], let [A=z C: Re(a+z) > Im(a+z)] and [B=z C: Re(a+z) 0]
  36. 436.Let w_1 be the point obtained by the rotation of z_1=5+4 i about the origin through a righ…
  37. 437.Let [C] be the circle in the complex plane with centre [z_0=(1)/(2)(1+3 i)] and radius r=1…
  38. 438.If the set Re(z-z+z z2-3 z+5 z): z C, Re(z)=3 is equal to the interval (, ], then 24(-) is…
  39. 439.If the center and radius of the circle [| z - 2 z - 3 | = 2] are respectively [(,)] and []…
  40. 440.For two non-zero complex numbers z_1 and z_2, if [Re(z_1 z_2)=0] and [Re(z_1+z_2)=0], then…
  41. 441.For all [z C] on the curve C_1:|z|=4, let the locus of the point [z+(1)/(z)] be the curve …
  42. 442.Let [a b] be two non-zero real numbers.
  43. 443.Let [A= (0,2 ): (1+2 i )/(1-i ).] is purely imaginary [].
  44. 444.If z is a complex number such that |z| 1, then the minimum value of |z+(1)/(2)(3+4 i)| is …
  45. 445.If [z=(1)/(2)-2 i] is such that [|z+1|= z+(1+i), i=-1] and [, R], then [+] is equal to
  46. 446.If [z=x+i y, x y 0], satisfies the equation [z^2+i z=0], then [|z^2|] is equal to :
  47. 447.Let z_1 and z_2 be two complex numbers such that z_1+z_2=5 and z_1^3+z_2^3=20+15 i Then, […
  48. 448.Consider the following two statements : Statement I: For any two non-zero complex numbers …
  49. 449.The sum of all possible values of [ [-, 2 ]], for which [(1+i )/(1-2 i )] is purely imagin…
  50. 450.If the set [R=(a, b): a+5 b=42, a, b N] has m elements and [_n=1^m(1-i^n !)=x+i y], where …